var bibbase_data = {"data":"<img src=\"//bibbase.org/img/ajax-loader.gif\" id=\"spinner\"\n  style=\"display: none;\" alt=\"Loading..\" />\n\n<div id=\"bibbase\">\n\n  <script type=\"text/javascript\">\n    var bibbase = {\n      params: {\"bib\":\"https://drive.google.com/uc?export=download&id=1NEXsxwRAx2CWt43v0y0jyZdP1LdOS_xF\",\"jsonp\":\"1\",\"authorFirst\":\"1\",\"sort\":\"-year\",\"theme\":\"side\",\"filter\":\"keywords:combinatorics\\\\b\",\"host\":\"bibbase.org\"},\n      data: [{\"bibtype\":\"article\",\"type\":\"article\",\"author\":[{\"firstnames\":[\"Toufik\"],\"propositions\":[],\"lastnames\":[\"Mansour\"],\"suffixes\":[]},{\"firstnames\":[\"Mark\"],\"propositions\":[],\"lastnames\":[\"Shattuck\"],\"suffixes\":[]},{\"firstnames\":[\"Mark\",\"C.\"],\"propositions\":[],\"lastnames\":[\"Wilson\"],\"suffixes\":[]}],\"title\":\"Congruence successions in compositions\",\"journal\":\"Discret. Math. Theor. Comput. Sci.\",\"volume\":\"16\",\"number\":\"1\",\"pages\":\"327-338\",\"year\":\"2014\",\"keywords\":\"combinatorics\",\"url\":\"http://dmtcs.episciences.org/1252\",\"abstract\":\"A \\\\emphcomposition is a sequence of positive integers, called \\\\emphparts, having a fixed sum. By an \\\\emph$m$-congruence succession, we will mean a pair of adjacent parts $x$ and $y$ within a composition such that $x≡ y (\\\\text{mod} m)$. Here, we consider the problem of counting the compositions of size $n$ according to the number of $m$-congruence successions, extending recent results concerning successions on subsets and permutations. A general formula is obtained, which reduces in the limiting case to the known generating function formula for the number of Carlitz compositions. Special attention is paid to the case $m=2$, where further enumerative results may be obtained by means of combinatorial arguments. Finally, an asymptotic estimate is provided for the number of compositions of size $n$ having no $m$-congruence successions.\",\"bibtex\":\"@article{MSW2014,\\n  author    = {Toufik Mansour and\\n               Mark Shattuck and\\n               Mark C. Wilson},\\n  title     = {Congruence successions in compositions},\\n  journal   = {Discret. Math. Theor. Comput. Sci.},\\n  volume    = {16},\\n  number    = {1},\\n  pages     = {327-338},\\n  year      = {2014},\\n  keywords={combinatorics},\\n  url       = {http://dmtcs.episciences.org/1252},\\n  abstract={A \\\\emph{composition} is a sequence of positive integers, called\\n\\\\emph{parts}, having a fixed sum.  By an \\\\emph{$m$-congruence\\nsuccession}, we will mean a pair of adjacent parts $x$ and $y$ within a\\ncomposition such that $x\\\\equiv y~(\\\\text{mod}~m)$.  Here, we consider the\\nproblem of counting the compositions of size $n$ according to the number\\nof $m$-congruence successions, extending recent results concerning\\nsuccessions on subsets and permutations.  A general formula is obtained,\\nwhich reduces in the limiting case to the known generating function\\nformula for the number of Carlitz compositions.  Special attention is\\npaid to the case $m=2$, where further enumerative results may be\\nobtained by means of combinatorial arguments.  Finally, an asymptotic\\nestimate is provided for the number of compositions of size $n$ having\\nno $m$-congruence successions.}\\n}\\n\\n\",\"author_short\":[\"Mansour, T.\",\"Shattuck, M.\",\"Wilson, M. C.\"],\"key\":\"MSW2014\",\"id\":\"MSW2014\",\"bibbaseid\":\"mansour-shattuck-wilson-congruencesuccessionsincompositions-2014\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://dmtcs.episciences.org/1252\"},\"keyword\":[\"combinatorics\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/networks/index.html\"}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Random Cayley digraphs of diameter 2 and given degree\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Širáň\"],\"firstnames\":[\"Jozef\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Potočnik\"],\"firstnames\":[\"Primož\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Lladser\"],\"firstnames\":[\"Manuel\",\"E.\"],\"suffixes\":[]}],\"journal\":\"Discrete Mathematics & Theoretical Computer Science\",\"volume\":\"14\",\"year\":\"2012\",\"publisher\":\"Episciences. org\",\"keywords\":\"combinatorics\",\"url_paper\":\"https://dmtcs.episciences.org/588/pdf\",\"abstract\":\"\",\"bibtex\":\"@article{wilson2012random,\\n  title={Random Cayley digraphs of diameter 2 and given degree},\\n  author={Wilson, Mark C. and {\\\\v{S}}ir{\\\\'a}{\\\\v{n}}, Jozef and Poto{\\\\v{c}}nik, Primo{\\\\v{z}} and Lladser, Manuel E.},\\n  journal={Discrete Mathematics \\\\& Theoretical Computer Science},\\n  volume={14},\\n  year={2012},\\n  publisher={Episciences. org},\\n  keywords={combinatorics},\\n  url_Paper={https://dmtcs.episciences.org/588/pdf},\\n  abstract={}\\n}\\n\\n\",\"author_short\":[\"Wilson, M. C.\",\"Širáň, J.\",\"Potočnik, P.\",\"Lladser, M. E.\"],\"key\":\"wilson2012random\",\"id\":\"wilson2012random\",\"bibbaseid\":\"wilson-ir-potonik-lladser-randomcayleydigraphsofdiameter2andgivendegree-2012\",\"role\":\"author\",\"urls\":{\" paper\":\"https://dmtcs.episciences.org/588/pdf\"},\"keyword\":[\"combinatorics\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/networks/index.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"An interesting new Mahonian permutation statistic\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"Electronic Journal of Combinatorics\",\"pages\":\"R147\",\"year\":\"2010\",\"keywords\":\"combinatorics\",\"url_paper\":\"https://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r147/pdf\",\"abstract\":\"The standard algorithm for generating a random permutation gives rise to an obvious permutation statistic DIS that is readily seen to be Mahonian. We give evidence showing that it is not equal to any previously published statistic. Nor does its joint distribution with the standard Eulerian statistics des and exc appear to coincide with any known Euler-Mahonian pair. A general construction of Skandera yields an Eulerian partner eul such that (eul, DIS) is equidistributed with (des, MAJ). However eul itself appears not to be a known Eulerian statistic. Several ideas for further research on this topic are listed.\",\"bibtex\":\"@article{wilson2010interesting,\\n  title={An interesting new Mahonian permutation statistic},\\n  author={Wilson, Mark C.},\\n  journal={Electronic Journal of Combinatorics},\\n  pages={R147},\\n  year={2010},\\n  keywords={combinatorics},\\n  url_Paper={https://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r147/pdf},\\n  abstract={The standard algorithm for generating a random permutation gives rise to\\nan obvious permutation statistic DIS that is readily seen to be\\nMahonian. We give evidence showing that it is not equal to any\\npreviously published statistic. Nor does its joint distribution with the\\nstandard Eulerian statistics des and exc appear to coincide with any\\nknown Euler-Mahonian pair.\\n\\nA general construction of Skandera yields an Eulerian partner eul such\\nthat (eul, DIS) is equidistributed with (des, MAJ). However eul itself\\nappears not to be a known Eulerian statistic.\\n\\nSeveral ideas for further research on this topic are listed.}\\n}\\n\\n\",\"author_short\":[\"Wilson, M. C.\"],\"key\":\"wilson2010interesting\",\"id\":\"wilson2010interesting\",\"bibbaseid\":\"wilson-aninterestingnewmahonianpermutationstatistic-2010\",\"role\":\"author\",\"urls\":{\" paper\":\"https://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r147/pdf\"},\"keyword\":[\"combinatorics\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/networks/index.html\"}},\"downloads\":3,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Random and exhaustive generation of permutations and cycles\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"Annals of Combinatorics\",\"volume\":\"12\",\"number\":\"4\",\"pages\":\"509-520\",\"year\":\"2009\",\"publisher\":\"SP Birkhäuser Verlag Basel\",\"keywords\":\"algorithms, combinatorics\",\"url_paper\":\"https://link.springer.com/content/pdf/10.1007/s00026-009-0003-3.pdf\",\"abstract\":\"In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. This algorithm is very similar to the standard method for generating a random permutation, but is less well known. We consider both methods in a unified way, and discuss their relation with exhaustive generation methods. We analyse several random variables associated with the algorithms and find their grand probability generating functions, which gives easy access to moments and limit laws.\",\"bibtex\":\"@article{wilson2009random,\\n  title={Random and exhaustive generation of permutations and cycles},\\n  author={Wilson, Mark C.},\\n  journal={Annals of Combinatorics},\\n  volume={12},\\n  number={4},\\n  pages={509-520},\\n  year={2009},\\n  publisher={SP Birkh{\\\\\\\"a}user Verlag Basel},\\n  keywords={algorithms, combinatorics},\\n  url_Paper={https://link.springer.com/content/pdf/10.1007/s00026-009-0003-3.pdf},\\n  abstract={In 1986 S. Sattolo introduced a simple algorithm for uniform random\\ngeneration of cyclic permutations on a fixed number of symbols. This\\nalgorithm is very similar to the standard method for generating a random\\npermutation, but is less well known. We consider both methods in a\\nunified way, and discuss their relation with exhaustive generation\\nmethods. We analyse several random variables associated with the\\nalgorithms and find their grand probability generating functions, which\\ngives easy access to moments and limit laws.}\\n}\\n\\n\",\"author_short\":[\"Wilson, M. C.\"],\"key\":\"wilson2009random\",\"id\":\"wilson2009random\",\"bibbaseid\":\"wilson-randomandexhaustivegenerationofpermutationsandcycles-2009\",\"role\":\"author\",\"urls\":{\" paper\":\"https://link.springer.com/content/pdf/10.1007/s00026-009-0003-3.pdf\"},\"keyword\":[\"algorithms\",\"combinatorics\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/networks/index.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Degree-and time-constrained broadcast networks\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Dinneen\"],\"firstnames\":[\"Michael\",\"J.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Pritchard\"],\"firstnames\":[\"Geoffrey\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"Networks\",\"volume\":\"39\",\"number\":\"3\",\"pages\":\"121-129\",\"year\":\"2002\",\"publisher\":\"Wiley\",\"keywords\":\"combinatorics, algorithms, graphs\",\"url_paper\":\"DPW2002.pdf\",\"abstract\":\"We consider the problem of constructing networks with as many nodes as possible, subject to upper bounds on the degree and broadcast time. The paper includes the results of an extensive empirical study of broadcasting in small regular graphs using a stochastic search algorithm to approximate the broadcast time. Significant improvements on known results are obtained for cubic broadcast networks.\",\"bibtex\":\"@article{dinneen2002degree,\\n  title={Degree-and time-constrained broadcast networks},\\n  author={Dinneen, Michael J. and Pritchard, Geoffrey and Wilson, Mark C.},\\n  journal={Networks},\\n  volume={39},\\n  number={3},\\n  pages={121-129},\\n  year={2002},\\n  publisher={Wiley},\\n  keywords={combinatorics, algorithms, graphs},\\n  url_Paper={DPW2002.pdf},\\n  abstract={We consider the problem of constructing networks with as many nodes as\\npossible, subject to upper bounds on the degree and broadcast time. The\\npaper includes the results of an extensive empirical study of\\nbroadcasting in small regular graphs using a stochastic search algorithm\\nto approximate the broadcast time. Significant improvements on known\\nresults are obtained for cubic broadcast networks.} \\n}\\n\\n\",\"author_short\":[\"Dinneen, M. J.\",\"Pritchard, G.\",\"Wilson, M. C.\"],\"key\":\"dinneen2002degree\",\"id\":\"dinneen2002degree\",\"bibbaseid\":\"dinneen-pritchard-wilson-degreeandtimeconstrainedbroadcastnetworks-2002\",\"role\":\"author\",\"urls\":{\" paper\":\"https://drive.google.com/DPW2002.pdf\"},\"keyword\":[\"combinatorics\",\"algorithms\",\"graphs\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/networks/index.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Construction of time-relaxed minimal broadcast networks\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Dinneen\"],\"firstnames\":[\"Michael\",\"J.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ventura\"],\"firstnames\":[\"Jose\",\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Zakeri\"],\"firstnames\":[\"Golbon\"],\"suffixes\":[]}],\"journal\":\"Parallel Processing Letters\",\"volume\":\"9\",\"number\":\"01\",\"pages\":\"53-68\",\"year\":\"1999\",\"publisher\":\"World Scientific Publishing Company\",\"keywords\":\"algorithms, combinatorics, graphs\",\"url_paper\":\"https://www.worldscientific.com/doi/abs/10.1142/S0129626499000086\",\"abstract\":\"In broadcasting, or one-to-all communication, a message originally held in one node of the network must be transmitted to all the other nodes. A minimal broadcast network is a communication network that can transmit a message originated at any node to all other nodes of the network in minimum time. In this paper, we present a compound method to construct sparse, time-relaxed, minimal broadcast networks ( $t$-mbn), in which broadcasting can be accomplished in slightly more than the minimum time. The proposed method generates a new network by connecting a subset of nodes from several copies of a $t_1$-mbn using the structure of another $t_2$-mbn. The objective is to construct a network as sparse as possible satisfying the desired broadcasting time constraint. Computational results illustrate the effectiveness of the proposed method.\",\"bibtex\":\"@article{dinneen1999construction,\\n  title={Construction of time-relaxed minimal broadcast networks},\\n  author={Dinneen, Michael J. and Ventura, Jose A. and Wilson, Mark C. and Zakeri, Golbon},\\n  journal={Parallel Processing Letters},\\n  volume={9},\\n  number={01},\\n  pages={53-68},\\n  year={1999},\\n  publisher={World Scientific Publishing Company},\\n  keywords={algorithms, combinatorics, graphs},\\n  url_Paper={https://www.worldscientific.com/doi/abs/10.1142/S0129626499000086},\\n  abstract={In broadcasting, or one-to-all communication, a message originally held\\nin one node of the network must be transmitted to all the other nodes. A\\nminimal broadcast network is a communication network that can transmit a\\nmessage originated at any node to all other nodes of the network in\\nminimum time. In this paper, we present a compound method to construct\\nsparse, time-relaxed, minimal broadcast networks ( $t$-mbn), in which\\nbroadcasting can be accomplished in slightly more than the minimum time.\\nThe proposed method generates a new network by connecting a subset of\\nnodes from several copies of a $t_1$-mbn using the structure of another\\n$t_2$-mbn. The objective is to construct a network as sparse as possible\\nsatisfying the desired broadcasting time constraint. Computational\\nresults illustrate the effectiveness of the proposed method.}\\n}\\n\\n\",\"author_short\":[\"Dinneen, M. J.\",\"Ventura, J. A.\",\"Wilson, M. C.\",\"Zakeri, G.\"],\"key\":\"dinneen1999construction\",\"id\":\"dinneen1999construction\",\"bibbaseid\":\"dinneen-ventura-wilson-zakeri-constructionoftimerelaxedminimalbroadcastnetworks-1999\",\"role\":\"author\",\"urls\":{\" paper\":\"https://www.worldscientific.com/doi/abs/10.1142/S0129626499000086\"},\"keyword\":[\"algorithms\",\"combinatorics\",\"graphs\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/networks/index.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Compound constructions of broadcast networks\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Dinneen\"],\"firstnames\":[\"Michael\",\"J.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ventura\"],\"firstnames\":[\"Jose\",\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Zakeri\"],\"firstnames\":[\"Golbon\"],\"suffixes\":[]}],\"journal\":\"Discrete Applied Mathematics\",\"volume\":\"93\",\"number\":\"2-3\",\"pages\":\"205-232\",\"year\":\"1999\",\"publisher\":\"North-Holland\",\"keywords\":\"algorithms, combinatorics, graphs\",\"url_paper\":\"https://www.sciencedirect.com/science/article/pii/S0166218X99000438\",\"abstract\":\"Compound methods have been shown to be very effective in the construction of minimal broadcast networks (mbns). Compound methods generate a large mbn by combining multiple copies of an mbn $G$ using the structure of another mbn $H$. Node deletion is also allowed in some of these methods. The subset of connecting nodes of $G$ has been defined as solid $h$-cover by Bermond, Fraigniaud and Peters, and center node set by Weng and Ventura. This article shows that the two concepts are equivalent. We also provide new properties for center node sets, including bounds on the minimum size of a center node set, show how to reduce the number of center nodes of an mbn generated by a compound method, and propose an iterative compounding algorithm that generates the sparsest known mbns in many cases.\",\"bibtex\":\"@article{dinneen1999compound,\\n  title={Compound constructions of broadcast networks},\\n  author={Dinneen, Michael J. and Ventura, Jose A. and Wilson, Mark C. and Zakeri, Golbon},\\n  journal={Discrete Applied Mathematics},\\n  volume={93},\\n  number={2-3},\\n  pages={205-232},\\n  year={1999},\\n  publisher={North-Holland},\\n  keywords={algorithms, combinatorics, graphs},\\n  url_Paper={https://www.sciencedirect.com/science/article/pii/S0166218X99000438},\\n  abstract={Compound methods have been shown to be very effective in the\\nconstruction of minimal broadcast networks (mbns). Compound methods\\ngenerate a large mbn by combining multiple copies of an mbn $G$ using\\nthe structure of another mbn $H$. Node deletion is also allowed in some\\nof these methods. The subset of connecting nodes of $G$ has been defined\\nas solid  $h$-cover by Bermond, Fraigniaud and Peters, and center node\\nset by Weng and Ventura. This article shows that the two concepts are\\nequivalent. We also provide new properties for center node sets,\\nincluding bounds on the minimum size of a center node set, show how to\\nreduce the number of center nodes of an mbn generated by a compound\\nmethod, and propose an iterative compounding algorithm that generates\\nthe sparsest known mbns in many cases.}\\n}\\n\\n\",\"author_short\":[\"Dinneen, M. J.\",\"Ventura, J. A.\",\"Wilson, M. C.\",\"Zakeri, G.\"],\"key\":\"dinneen1999compound\",\"id\":\"dinneen1999compound\",\"bibbaseid\":\"dinneen-ventura-wilson-zakeri-compoundconstructionsofbroadcastnetworks-1999\",\"role\":\"author\",\"urls\":{\" paper\":\"https://www.sciencedirect.com/science/article/pii/S0166218X99000438\"},\"keyword\":[\"algorithms\",\"combinatorics\",\"graphs\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/networks/index.html\"}},\"html\":\"\"}],\n      metadata: {\"owner\":\"wilson, m\",\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/networks/index.html\"}},\n      ownerID: \"X59RJvnvQGf3jqFj4\"\n    };\n  </script>\n\n  <script type=\"text/javascript\">\n  var site$;\n  if (typeof $ != 'undefined') {\n    console.log('existing jquery: storing and then restoring');\n    site$ = $;\n    $ = null;\n  }\n  </script>\n\n  <script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.2.4/jquery.min.js\">\n  </script>\n  <script type=\"text/javascript\">\n  if (site$) {\n    console.log('existing jquery: avoiding conflict and restoring');\n    bb$ = $.noConflict(true);\n    $ = site$;\n  } else {\n    bb$ = $;\n  }\n  </script>\n\n  <script src=\"//bibbase.org/js/bibbase.min.js\"\n          type=\"text/javascript\">\n  </script>\n\n  <script type=\"text/javascript\"\n          src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML\">\n  </script>\n  <script type=\"text/x-mathjax-config\">\n    MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\\\(','\\\\)']]},\n                        skipTags: [\"body\"],\n                        processClass: \"bibbase_paper\"});\n  </script>\n\n  <style>\n  @media print {\n    .dontprint {\n        display: none !important;\n    }\n\n  .bibbase_group {\n    background-color: #E0E0E0;\n    font-style: italic;\n    font-size: larger;\n    text-shadow: 0px 0px 3px #FFFFFF;\n    border-radius: 4px 4px 4px 4px;\n    -moz-border-radius: 4px 4px 4px 4px;\n    -webkit-border-radius: 4px;\n    padding: 5px 40px 5px;\n    margin-top: 10px;\n    margin-bottom: 5px;\n    cursor: pointer;\n  }\n\n  .bibbase_paper {\n    margin-bottom: 5px;\n  }\n\n  }\n  </style>\n\n  \n  <div style=\"float: right; margin-right: 10px; margin-top: 10px; text-align: right; font-size: 12px\">\n    generated by\n    <a href=\"//bibbase.org\"\n       onclick=\"trackOutboundLink('bibbase', 'logo clicked', window.location.href, '//bibbase.org'); return false;\">\n      <img src=\"//bibbase.org/img/logo.svg\"\n           style=\"vertical-align: middle; margin-left: 3px; height: 16px;\"/\n           alt=\"bibbase.org\"\n           title=\"BibBase – The easiest way to maintain your publications page.\"\n        ></a>\n    \n  </div>\n  \n\n  <div id=\"bibbase_header\" class=\"dontprint\" style=\"\">\n\n    <ul class=\"nav nav-pills\" style=\"margin: 0px;\">\n\n      <li class=\"dropdown\" id=\"groupby_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\">\n          Group by\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li class=\"groupby year\"><a onclick=\"groupby('year')\">\n            Year</a>\n        </li>\n        <li class=\"groupby author\"><a onclick=\"groupby('author_short')\">\n            Author</a>\n        </li>\n        <li class=\"groupby type\"><a onclick=\"groupby('type')\">\n            Type</a>\n        </li>\n        <li class=\"groupby keyword\"><a onclick=\"groupby('keyword')\">\n            Keyword</a>\n        </li>\n        <li class=\"groupby downloads\"><a onclick=\"groupby('downloads')\">\n            Downloads</a>\n        </li>\n      </ul>\n      </li>\n\n\n      <li class=\"dropdown\" id=\"menu_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\" alt=\"controls\">\n          <i class=\"fa fa-reorder\" alt=\"controls\"></i>\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li>\n          <a onclick=\"toggleAll()\">\n            <i class=\"fa fa-chevron-down fa-fw\"></i> Expand/Collapse All\n          </a>\n        </li>\n        <li>\n          <a download=\"uc\" href=\"data:text/bibtex;base64,@article{MSW2014,
  author    = {Toufik Mansour and
               Mark Shattuck and
               Mark C. Wilson},
  title     = {Congruence successions in compositions},
  journal   = {Discret. Math. Theor. Comput. Sci.},
  volume    = {16},
  number    = {1},
  pages     = {327-338},
  year      = {2014},
  keywords={combinatorics},
  url       = {http://dmtcs.episciences.org/1252},
  abstract={A \emph{composition} is a sequence of positive integers, called
\emph{parts}, having a fixed sum.  By an \emph{$m$-congruence
succession}, we will mean a pair of adjacent parts $x$ and $y$ within a
composition such that $x\equiv y~(\text{mod}~m)$.  Here, we consider the
problem of counting the compositions of size $n$ according to the number
of $m$-congruence successions, extending recent results concerning
successions on subsets and permutations.  A general formula is obtained,
which reduces in the limiting case to the known generating function
formula for the number of Carlitz compositions.  Special attention is
paid to the case $m=2$, where further enumerative results may be
obtained by means of combinatorial arguments.  Finally, an asymptotic
estimate is provided for the number of compositions of size $n$ having
no $m$-congruence successions.}
}



@article{wilson2012random,
  title={Random Cayley digraphs of diameter 2 and given degree},
  author={Wilson, Mark C. and {\v{S}}ir{\'a}{\v{n}}, Jozef and Poto{\v{c}}nik, Primo{\v{z}} and Lladser, Manuel E.},
  journal={Discrete Mathematics \& Theoretical Computer Science},
  volume={14},
  year={2012},
  publisher={Episciences. org},
  keywords={combinatorics},
  url_Paper={https://dmtcs.episciences.org/588/pdf},
  abstract={}
}



@article{wilson2010interesting,
  title={An interesting new Mahonian permutation statistic},
  author={Wilson, Mark C.},
  journal={Electronic Journal of Combinatorics},
  pages={R147},
  year={2010},
  keywords={combinatorics},
  url_Paper={https://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r147/pdf},
  abstract={The standard algorithm for generating a random permutation gives rise to
an obvious permutation statistic DIS that is readily seen to be
Mahonian. We give evidence showing that it is not equal to any
previously published statistic. Nor does its joint distribution with the
standard Eulerian statistics des and exc appear to coincide with any
known Euler-Mahonian pair.

A general construction of Skandera yields an Eulerian partner eul such
that (eul, DIS) is equidistributed with (des, MAJ). However eul itself
appears not to be a known Eulerian statistic.

Several ideas for further research on this topic are listed.}
}



@article{wilson2009random,
  title={Random and exhaustive generation of permutations and cycles},
  author={Wilson, Mark C.},
  journal={Annals of Combinatorics},
  volume={12},
  number={4},
  pages={509-520},
  year={2009},
  publisher={SP Birkh{\"a}user Verlag Basel},
  keywords={algorithms, combinatorics},
  url_Paper={https://link.springer.com/content/pdf/10.1007/s00026-009-0003-3.pdf},
  abstract={In 1986 S. Sattolo introduced a simple algorithm for uniform random
generation of cyclic permutations on a fixed number of symbols. This
algorithm is very similar to the standard method for generating a random
permutation, but is less well known. We consider both methods in a
unified way, and discuss their relation with exhaustive generation
methods. We analyse several random variables associated with the
algorithms and find their grand probability generating functions, which
gives easy access to moments and limit laws.}
}



@article{dinneen2002degree,
  title={Degree-and time-constrained broadcast networks},
  author={Dinneen, Michael J. and Pritchard, Geoffrey and Wilson, Mark C.},
  journal={Networks},
  volume={39},
  number={3},
  pages={121-129},
  year={2002},
  publisher={Wiley},
  keywords={combinatorics, algorithms, graphs},
  url_Paper={DPW2002.pdf},
  abstract={We consider the problem of constructing networks with as many nodes as
possible, subject to upper bounds on the degree and broadcast time. The
paper includes the results of an extensive empirical study of
broadcasting in small regular graphs using a stochastic search algorithm
to approximate the broadcast time. Significant improvements on known
results are obtained for cubic broadcast networks.} 
}



@article{dinneen1999construction,
  title={Construction of time-relaxed minimal broadcast networks},
  author={Dinneen, Michael J. and Ventura, Jose A. and Wilson, Mark C. and Zakeri, Golbon},
  journal={Parallel Processing Letters},
  volume={9},
  number={01},
  pages={53-68},
  year={1999},
  publisher={World Scientific Publishing Company},
  keywords={algorithms, combinatorics, graphs},
  url_Paper={https://www.worldscientific.com/doi/abs/10.1142/S0129626499000086},
  abstract={In broadcasting, or one-to-all communication, a message originally held
in one node of the network must be transmitted to all the other nodes. A
minimal broadcast network is a communication network that can transmit a
message originated at any node to all other nodes of the network in
minimum time. In this paper, we present a compound method to construct
sparse, time-relaxed, minimal broadcast networks ( $t$-mbn), in which
broadcasting can be accomplished in slightly more than the minimum time.
The proposed method generates a new network by connecting a subset of
nodes from several copies of a $t_1$-mbn using the structure of another
$t_2$-mbn. The objective is to construct a network as sparse as possible
satisfying the desired broadcasting time constraint. Computational
results illustrate the effectiveness of the proposed method.}
}



@article{dinneen1999compound,
  title={Compound constructions of broadcast networks},
  author={Dinneen, Michael J. and Ventura, Jose A. and Wilson, Mark C. and Zakeri, Golbon},
  journal={Discrete Applied Mathematics},
  volume={93},
  number={2-3},
  pages={205-232},
  year={1999},
  publisher={North-Holland},
  keywords={algorithms, combinatorics, graphs},
  url_Paper={https://www.sciencedirect.com/science/article/pii/S0166218X99000438},
  abstract={Compound methods have been shown to be very effective in the
construction of minimal broadcast networks (mbns). Compound methods
generate a large mbn by combining multiple copies of an mbn $G$ using
the structure of another mbn $H$. Node deletion is also allowed in some
of these methods. The subset of connecting nodes of $G$ has been defined
as solid  $h$-cover by Bermond, Fraigniaud and Peters, and center node
set by Weng and Ventura. This article shows that the two concepts are
equivalent. We also provide new properties for center node sets,
including bounds on the minimum size of a center node set, show how to
reduce the number of center nodes of an mbn generated by a compound
method, and propose an iterative compounding algorithm that generates
the sparsest known mbns in many cases.}
}

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C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://dmtcs.episciences.org/1252\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'mansour-shattuck-wilson-congruencesuccessionsincompositions-2014', 'http://dmtcs.episciences.org/1252', event);\">\n    Congruence successions in compositions.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Discret. Math. Theor. Comput. Sci.</i>, 16(1): 327-338.  2014.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://dmtcs.episciences.org/1252\"\n     onclick=\"log_download('mansour-shattuck-wilson-congruencesuccessionsincompositions-2014', 'http://dmtcs.episciences.org/1252', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Congruence successions in compositions [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/mansour-shattuck-wilson-congruencesuccessionsincompositions-2014\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('mansour-shattuck-wilson-congruencesuccessionsincompositions-2014')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{MSW2014,\n  author    = {Toufik Mansour and\n               Mark Shattuck and\n               Mark C. Wilson},\n  title     = {Congruence successions in compositions},\n  journal   = {Discret. Math. Theor. Comput. Sci.},\n  volume    = {16},\n  number    = {1},\n  pages     = {327-338},\n  year      = {2014},\n  keywords={combinatorics},\n  url       = {http://dmtcs.episciences.org/1252},\n  abstract={A \\emph{composition} is a sequence of positive integers, called\n\\emph{parts}, having a fixed sum.  By an \\emph{$m$-congruence\nsuccession}, we will mean a pair of adjacent parts $x$ and $y$ within a\ncomposition such that $x\\equiv y~(\\text{mod}~m)$.  Here, we consider the\nproblem of counting the compositions of size $n$ according to the number\nof $m$-congruence successions, extending recent results concerning\nsuccessions on subsets and permutations.  A general formula is obtained,\nwhich reduces in the limiting case to the known generating function\nformula for the number of Carlitz compositions.  Special attention is\npaid to the case $m=2$, where further enumerative results may be\nobtained by means of combinatorial arguments.  Finally, an asymptotic\nestimate is provided for the number of compositions of size $n$ having\nno $m$-congruence successions.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  A \\emphcomposition is a sequence of positive integers, called \\emphparts, having a fixed sum. By an \\emph$m$-congruence succession, we will mean a pair of adjacent parts $x$ and $y$ within a composition such that $x≡ y (\\text{mod} m)$. Here, we consider the problem of counting the compositions of size $n$ according to the number of $m$-congruence successions, extending recent results concerning successions on subsets and permutations. A general formula is obtained, which reduces in the limiting case to the known generating function formula for the number of Carlitz compositions. Special attention is paid to the case $m=2$, where further enumerative results may be obtained by means of combinatorial arguments. Finally, an asymptotic estimate is provided for the number of compositions of size $n$ having no $m$-congruence successions.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2012\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2012')\"\n      onkeypress=\"toggleGroup('group_2012')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2012</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"wilson-ir-potonik-lladser-randomcayleydigraphsofdiameter2andgivendegree-2012\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/networks/index.html\">Wilson, M. C.</a>; Širáň, J.; Potočnik, P.;  and Lladser, M. E.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://dmtcs.episciences.org/588/pdf\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'wilson-ir-potonik-lladser-randomcayleydigraphsofdiameter2andgivendegree-2012', 'https://dmtcs.episciences.org/588/pdf', event);\">\n    Random Cayley digraphs of diameter 2 and given degree.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Discrete Mathematics & Theoretical Computer Science</i>, 14.  2012.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://dmtcs.episciences.org/588/pdf\"\n     onclick=\"log_download('wilson-ir-potonik-lladser-randomcayleydigraphsofdiameter2andgivendegree-2012', 'https://dmtcs.episciences.org/588/pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Random Cayley digraphs of diameter 2 and given degree [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/wilson-ir-potonik-lladser-randomcayleydigraphsofdiameter2andgivendegree-2012\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('wilson-ir-potonik-lladser-randomcayleydigraphsofdiameter2andgivendegree-2012')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{wilson2012random,\n  title={Random Cayley digraphs of diameter 2 and given degree},\n  author={Wilson, Mark C. and {\\v{S}}ir{\\&#x27;a}{\\v{n}}, Jozef and Poto{\\v{c}}nik, Primo{\\v{z}} and Lladser, Manuel E.},\n  journal={Discrete Mathematics \\&amp; Theoretical Computer Science},\n  volume={14},\n  year={2012},\n  publisher={Episciences. org},\n  keywords={combinatorics},\n  url_Paper={https://dmtcs.episciences.org/588/pdf},\n  abstract={}\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2010\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2010')\"\n      onkeypress=\"toggleGroup('group_2010')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2010</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"wilson-aninterestingnewmahonianpermutationstatistic-2010\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/networks/index.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r147/pdf\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'wilson-aninterestingnewmahonianpermutationstatistic-2010', 'https://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r147/pdf', event);\">\n    An interesting new Mahonian permutation statistic.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Electronic Journal of Combinatorics</i>,R147.  2010.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r147/pdf\"\n     onclick=\"log_download('wilson-aninterestingnewmahonianpermutationstatistic-2010', 'https://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r147/pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"An interesting new Mahonian permutation statistic [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/wilson-aninterestingnewmahonianpermutationstatistic-2010\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>3 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('wilson-aninterestingnewmahonianpermutationstatistic-2010')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{wilson2010interesting,\n  title={An interesting new Mahonian permutation statistic},\n  author={Wilson, Mark C.},\n  journal={Electronic Journal of Combinatorics},\n  pages={R147},\n  year={2010},\n  keywords={combinatorics},\n  url_Paper={https://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1r147/pdf},\n  abstract={The standard algorithm for generating a random permutation gives rise to\nan obvious permutation statistic DIS that is readily seen to be\nMahonian. We give evidence showing that it is not equal to any\npreviously published statistic. Nor does its joint distribution with the\nstandard Eulerian statistics des and exc appear to coincide with any\nknown Euler-Mahonian pair.\n\nA general construction of Skandera yields an Eulerian partner eul such\nthat (eul, DIS) is equidistributed with (des, MAJ). However eul itself\nappears not to be a known Eulerian statistic.\n\nSeveral ideas for further research on this topic are listed.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The standard algorithm for generating a random permutation gives rise to an obvious permutation statistic DIS that is readily seen to be Mahonian. We give evidence showing that it is not equal to any previously published statistic. Nor does its joint distribution with the standard Eulerian statistics des and exc appear to coincide with any known Euler-Mahonian pair. A general construction of Skandera yields an Eulerian partner eul such that (eul, DIS) is equidistributed with (des, MAJ). However eul itself appears not to be a known Eulerian statistic. Several ideas for further research on this topic are listed.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2009\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2009')\"\n      onkeypress=\"toggleGroup('group_2009')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2009</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"wilson-randomandexhaustivegenerationofpermutationsandcycles-2009\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/networks/index.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://link.springer.com/content/pdf/10.1007/s00026-009-0003-3.pdf\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'wilson-randomandexhaustivegenerationofpermutationsandcycles-2009', 'https://link.springer.com/content/pdf/10.1007/s00026-009-0003-3.pdf', event);\">\n    Random and exhaustive generation of permutations and cycles.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Annals of Combinatorics</i>, 12(4): 509-520.  2009.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://link.springer.com/content/pdf/10.1007/s00026-009-0003-3.pdf\"\n     onclick=\"log_download('wilson-randomandexhaustivegenerationofpermutationsandcycles-2009', 'https://link.springer.com/content/pdf/10.1007/s00026-009-0003-3.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Random and exhaustive generation of permutations and cycles [pdf]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/wilson-randomandexhaustivegenerationofpermutationsandcycles-2009\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('wilson-randomandexhaustivegenerationofpermutationsandcycles-2009')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{wilson2009random,\n  title={Random and exhaustive generation of permutations and cycles},\n  author={Wilson, Mark C.},\n  journal={Annals of Combinatorics},\n  volume={12},\n  number={4},\n  pages={509-520},\n  year={2009},\n  publisher={SP Birkh{\\&quot;a}user Verlag Basel},\n  keywords={algorithms, combinatorics},\n  url_Paper={https://link.springer.com/content/pdf/10.1007/s00026-009-0003-3.pdf},\n  abstract={In 1986 S. Sattolo introduced a simple algorithm for uniform random\ngeneration of cyclic permutations on a fixed number of symbols. This\nalgorithm is very similar to the standard method for generating a random\npermutation, but is less well known. We consider both methods in a\nunified way, and discuss their relation with exhaustive generation\nmethods. We analyse several random variables associated with the\nalgorithms and find their grand probability generating functions, which\ngives easy access to moments and limit laws.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. This algorithm is very similar to the standard method for generating a random permutation, but is less well known. We consider both methods in a unified way, and discuss their relation with exhaustive generation methods. We analyse several random variables associated with the algorithms and find their grand probability generating functions, which gives easy access to moments and limit laws.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2002\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2002')\"\n      onkeypress=\"toggleGroup('group_2002')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2002</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"dinneen-pritchard-wilson-degreeandtimeconstrainedbroadcastnetworks-2002\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Dinneen, M. J.; Pritchard, G.;  and <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/networks/index.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://drive.google.com/DPW2002.pdf\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'dinneen-pritchard-wilson-degreeandtimeconstrainedbroadcastnetworks-2002', 'https://drive.google.com/DPW2002.pdf', event);\">\n    Degree-and time-constrained broadcast networks.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Networks</i>, 39(3): 121-129.  2002.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://drive.google.com/DPW2002.pdf\"\n     onclick=\"log_download('dinneen-pritchard-wilson-degreeandtimeconstrainedbroadcastnetworks-2002', 'https://drive.google.com/DPW2002.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Degree-and time-constrained broadcast networks [pdf]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/dinneen-pritchard-wilson-degreeandtimeconstrainedbroadcastnetworks-2002\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('dinneen-pritchard-wilson-degreeandtimeconstrainedbroadcastnetworks-2002')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{dinneen2002degree,\n  title={Degree-and time-constrained broadcast networks},\n  author={Dinneen, Michael J. and Pritchard, Geoffrey and Wilson, Mark C.},\n  journal={Networks},\n  volume={39},\n  number={3},\n  pages={121-129},\n  year={2002},\n  publisher={Wiley},\n  keywords={combinatorics, algorithms, graphs},\n  url_Paper={DPW2002.pdf},\n  abstract={We consider the problem of constructing networks with as many nodes as\npossible, subject to upper bounds on the degree and broadcast time. The\npaper includes the results of an extensive empirical study of\nbroadcasting in small regular graphs using a stochastic search algorithm\nto approximate the broadcast time. Significant improvements on known\nresults are obtained for cubic broadcast networks.} \n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We consider the problem of constructing networks with as many nodes as possible, subject to upper bounds on the degree and broadcast time. The paper includes the results of an extensive empirical study of broadcasting in small regular graphs using a stochastic search algorithm to approximate the broadcast time. Significant improvements on known results are obtained for cubic broadcast networks.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1999\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1999')\"\n      onkeypress=\"toggleGroup('group_1999')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1999</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"dinneen-ventura-wilson-zakeri-constructionoftimerelaxedminimalbroadcastnetworks-1999\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Dinneen, M. J.; Ventura, J. A.; <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/networks/index.html\">Wilson, M. C.</a>;  and Zakeri, G.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.worldscientific.com/doi/abs/10.1142/S0129626499000086\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'dinneen-ventura-wilson-zakeri-constructionoftimerelaxedminimalbroadcastnetworks-1999', 'https://www.worldscientific.com/doi/abs/10.1142/S0129626499000086', event);\">\n    Construction of time-relaxed minimal broadcast networks.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Parallel Processing Letters</i>, 9(01): 53-68.  1999.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.worldscientific.com/doi/abs/10.1142/S0129626499000086\"\n     onclick=\"log_download('dinneen-ventura-wilson-zakeri-constructionoftimerelaxedminimalbroadcastnetworks-1999', 'https://www.worldscientific.com/doi/abs/10.1142/S0129626499000086', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Construction of time-relaxed minimal broadcast networks [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/dinneen-ventura-wilson-zakeri-constructionoftimerelaxedminimalbroadcastnetworks-1999\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('dinneen-ventura-wilson-zakeri-constructionoftimerelaxedminimalbroadcastnetworks-1999')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{dinneen1999construction,\n  title={Construction of time-relaxed minimal broadcast networks},\n  author={Dinneen, Michael J. and Ventura, Jose A. and Wilson, Mark C. and Zakeri, Golbon},\n  journal={Parallel Processing Letters},\n  volume={9},\n  number={01},\n  pages={53-68},\n  year={1999},\n  publisher={World Scientific Publishing Company},\n  keywords={algorithms, combinatorics, graphs},\n  url_Paper={https://www.worldscientific.com/doi/abs/10.1142/S0129626499000086},\n  abstract={In broadcasting, or one-to-all communication, a message originally held\nin one node of the network must be transmitted to all the other nodes. A\nminimal broadcast network is a communication network that can transmit a\nmessage originated at any node to all other nodes of the network in\nminimum time. In this paper, we present a compound method to construct\nsparse, time-relaxed, minimal broadcast networks ( $t$-mbn), in which\nbroadcasting can be accomplished in slightly more than the minimum time.\nThe proposed method generates a new network by connecting a subset of\nnodes from several copies of a $t_1$-mbn using the structure of another\n$t_2$-mbn. The objective is to construct a network as sparse as possible\nsatisfying the desired broadcasting time constraint. Computational\nresults illustrate the effectiveness of the proposed method.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In broadcasting, or one-to-all communication, a message originally held in one node of the network must be transmitted to all the other nodes. A minimal broadcast network is a communication network that can transmit a message originated at any node to all other nodes of the network in minimum time. In this paper, we present a compound method to construct sparse, time-relaxed, minimal broadcast networks ( $t$-mbn), in which broadcasting can be accomplished in slightly more than the minimum time. The proposed method generates a new network by connecting a subset of nodes from several copies of a $t_1$-mbn using the structure of another $t_2$-mbn. The objective is to construct a network as sparse as possible satisfying the desired broadcasting time constraint. Computational results illustrate the effectiveness of the proposed method.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"dinneen-ventura-wilson-zakeri-compoundconstructionsofbroadcastnetworks-1999\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Dinneen, M. J.; Ventura, J. A.; <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/networks/index.html\">Wilson, M. C.</a>;  and Zakeri, G.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0166218X99000438\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'dinneen-ventura-wilson-zakeri-compoundconstructionsofbroadcastnetworks-1999', 'https://www.sciencedirect.com/science/article/pii/S0166218X99000438', event);\">\n    Compound constructions of broadcast networks.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Discrete Applied Mathematics</i>, 93(2-3): 205-232.  1999.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0166218X99000438\"\n     onclick=\"log_download('dinneen-ventura-wilson-zakeri-compoundconstructionsofbroadcastnetworks-1999', 'https://www.sciencedirect.com/science/article/pii/S0166218X99000438', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Compound constructions of broadcast networks [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/dinneen-ventura-wilson-zakeri-compoundconstructionsofbroadcastnetworks-1999\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('dinneen-ventura-wilson-zakeri-compoundconstructionsofbroadcastnetworks-1999')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{dinneen1999compound,\n  title={Compound constructions of broadcast networks},\n  author={Dinneen, Michael J. and Ventura, Jose A. and Wilson, Mark C. and Zakeri, Golbon},\n  journal={Discrete Applied Mathematics},\n  volume={93},\n  number={2-3},\n  pages={205-232},\n  year={1999},\n  publisher={North-Holland},\n  keywords={algorithms, combinatorics, graphs},\n  url_Paper={https://www.sciencedirect.com/science/article/pii/S0166218X99000438},\n  abstract={Compound methods have been shown to be very effective in the\nconstruction of minimal broadcast networks (mbns). Compound methods\ngenerate a large mbn by combining multiple copies of an mbn $G$ using\nthe structure of another mbn $H$. Node deletion is also allowed in some\nof these methods. The subset of connecting nodes of $G$ has been defined\nas solid  $h$-cover by Bermond, Fraigniaud and Peters, and center node\nset by Weng and Ventura. This article shows that the two concepts are\nequivalent. We also provide new properties for center node sets,\nincluding bounds on the minimum size of a center node set, show how to\nreduce the number of center nodes of an mbn generated by a compound\nmethod, and propose an iterative compounding algorithm that generates\nthe sparsest known mbns in many cases.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Compound methods have been shown to be very effective in the construction of minimal broadcast networks (mbns). Compound methods generate a large mbn by combining multiple copies of an mbn $G$ using the structure of another mbn $H$. Node deletion is also allowed in some of these methods. The subset of connecting nodes of $G$ has been defined as solid $h$-cover by Bermond, Fraigniaud and Peters, and center node set by Weng and Ventura. This article shows that the two concepts are equivalent. We also provide new properties for center node sets, including bounds on the minimum size of a center node set, show how to reduce the number of center nodes of an mbn generated by a compound method, and propose an iterative compounding algorithm that generates the sparsest known mbns in many cases.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n\n\n\n  </div>\n\n\n  <!-- Modal -->\n\n  <!-- <iframe id=\"bibbase_network_frame\" -->\n  <!--         src=\"//bibbase.org/network/control\" -->\n  <!--         style=\"display: none;\"> -->\n  <!-- </iframe> -->\n\n</div>\n"}; document.write(bibbase_data.data);