The asymptotic distribution of the rank for unimodal sequences

JOURNAL OF NUMBER THEORY

卷:229

Article

Bringmann, Kathrin¹  Jennings-Shaffer, Chris¹  Mahlburg, Karl² 

[1] Univ Cologne, Dept Math & Comp Sci, Weyertal 86-90, D-50931 Cologne, Germany

[2] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

关键词: Integer partitions;    Unimodal sequences;    Asymptotics;    Distributions;    Probabilistic methods;    Modular forms;    Mock modular forms;   

DOI  :  10.1016/j.jnt.2020.11.016

来源: Elsevier

【 摘 要 】

We study the asymptotic behavior of the rank statistic for unimodal sequences. We use analytic techniques involving asymptotic expansions in order to prove asymptotic formulas for the moments of the rank. Furthermore, when appropriately normalized, the values of the unimodal rank asymptotically follow a logistic distribution. We also prove similar results for Durfee unimodal sequences and semi-strict unimodal sequences, with the only major difference being that the (normalized) rank for semistrict unimodal sequences has a distributional limit of a point mass probability distribution. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free