Asymptotic formulas for stacks and unimodal sequences

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:126

Article

Bringmann, Kathrin¹  Mahlburg, Karl² 

[1] Univ Cologne, Math Inst, D-50931 Cologne, Germany

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

关键词: Unimodal sequences;    Generating functions;    Asymptotic formulas;    Integer partitions;    Tauberian theorems;   

DOI  :  10.1016/j.jcta.2014.04.006

来源: Elsevier

【 摘 要 】

We study enumeration functions for unimodal sequences of positive integers, where the size of a sequence is the sum of its terms. We survey known results for a number of natural variants of unimodal sequences, including Auluck's generalized Ferrers diagrams, Wright's stacks, and Andrews' convex compositions. These results describe combinatorial properties, generating functions, and asymptotic formulas for the enumeration functions. We also prove several new asymptotic results that fill in the notable missing cases from the literature, including an open problem in statistical mechanics due to Temperley. Furthermore, we explain the combinatorial and asymptotic relationship between partitions, Andrews' Frobenius symbols, and stacks with summits. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free