Asymptotics of coefficients of algebraic series via embedding into rational series (extended abstract). Greenwood, T., Melczer, S., Ruza, T., & Wilson, M. C. Séminaire Lotharingien de Combinatoire, 86B:12pp, 2022. Paper Slides abstract bibtex 9 downloads We present a strategy for computing asymptotics of coefficients of $d$-variate algebraic generating functions. Using known constructions, we embed the coefficient array into an array represented by a rational generating functions in $d+1$ variables, and then apply ACSV theory to analyse the latter. This method allows us to give systematic results in the multivariate case, seems more promising than trying to derive analogs of the rational ACSV theory for algebraic GFs, and gives the prospect of further improvements as embedding methods are studied in more detail.
@Article{GMRW2022,
author = {Greenwood, Torin and Melczer, Stephen and Ruza, Tiadora and Wilson, Mark C.},
journal = {S\'{e}minaire Lotharingien de Combinatoire},
abstract = {We present a strategy for computing asymptotics of coefficients of
$d$-variate algebraic generating functions. Using known constructions,
we embed the coefficient array into an array represented by a rational
generating functions in $d+1$ variables, and then apply ACSV theory to
analyse the latter. This method allows us to give systematic results in
the multivariate case, seems more promising than trying to derive
analogs of the rational ACSV theory for algebraic GFs, and gives the
prospect of further improvements as embedding methods are studied in
more detail.},
title = {Asymptotics of coefficients of algebraic series via embedding into rational series (extended abstract)},
year = {2022},
pages = {12pp},
volume = {86B},
keywords={ACSV applications, ACSV theory},
url_paper = {https://www.emis.de/journals/SLC/wpapers/FPSAC2022/30.pdf},
url_slides = {},
}
Downloads: 9
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