@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.}
}

{"_id":"hyaRqGTYR5t8CtnPA","bibbaseid":"mansour-shattuck-wilson-congruencesuccessionsincompositions-2014","author_short":["Mansour, T.","Shattuck, M.","Wilson, M. C."],"bibdata":{"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":{}},"downloads":3},"bibtype":"article","biburl":"https://drive.google.com/uc?export=download&id=1NEXsxwRAx2CWt43v0y0jyZdP1LdOS_xF","dataSources":["AJqx2GM6kFj3JDh8G","yx9ivfGLzvFNsg4LH","QdFdNQZBZSvbPbp7t","o2FBsFrZMS3PxguCG","SjBh38uzaGjRinwq8","M2T285kj8vXfTkGDx","2zimNJgtWEiEM2L3J","TAyBmAZAcnenc4YET","BCqQErP8wgW48bwvt","YjweTJPHHEQ85Pems"],"keywords":["combinatorics"],"search_terms":["congruence","successions","compositions","mansour","shattuck","wilson"],"title":"Congruence successions in compositions","year":2014,"downloads":3}