Diagonal asymptotics for symmetric rational functions via ACSV

Yuliy Baryshnikov, Stephen Melczer, Robin Pemantle, Armin Straub

研究成果: 書籍/レポート タイプへの寄稿会議への寄与

1 被引用数 (Scopus)

抄録

We consider asymptotics of power series coefficients of rational functions of the form 1/Q where Q is a symmetric multilinear polynomial. We review a number of such cases from the literature, chiefly concerned either with positivity of coefficients or diagonal asymptotics. We then analyze coefficient asymptotics using ACSV (Analytic Combinatorics in Several Variables) methods. While ACSV sometimes requires considerable overhead and geometric computation, in the case of symmetric multilinear rational functions there are some reductions that streamline the analysis. Our results include diagonal asymptotics across entire classes of functions, for example the general 3-variable case and the Gillis-Reznick-Zeilberger (GRZ) case, where the denominator in terms of elementary symmetric functions is 1-e1 +ced in any number d of variables. The ACSV analysis also explains a discontinuous drop in exponential growth rate for the GRZ class at the parameter value c = (d - 1)d-1, previously observed for d = 4 only by separately computing diagonal recurrences for critical and noncritical values of c.

本文言語英語
ホスト出版物のタイトル29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, AofA 2018
編集者Mark Daniel Ward, James Allen Fill
出版社Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN(電子版)9783959770781
DOI
出版ステータス出版済み - 6月 1 2018
外部発表はい
イベント29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, AofA 2018 - Uppsala, スウェーデン
継続期間: 6月 25 20186月 29 2018

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
110
ISSN(印刷版)1868-8969

会議

会議29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, AofA 2018
国/地域スウェーデン
CityUppsala
Period6/25/186/29/18

!!!All Science Journal Classification (ASJC) codes

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