Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.jcta.2014.04.006 | Journal of Combinatorial Theory, Series A |
Keywords | Field | DocType |
Unimodal sequences,Generating functions,Asymptotic formulas,Integer partitions,Tauberian theorems | Abelian and tauberian theorems,Integer,Discrete mathematics,Generating function,Combinatorics,Statistical mechanics,Open problem,Enumeration,Regular polygon,Partition (number theory),Mathematics | Journal |
Volume | ISSN | Citations |
126 | 0097-3165 | 1 |
PageRank | References | Authors |
0.67 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kathrin Bringmann | 1 | 3 | 4.87 |
| Karl Mahlburg | 2 | 13 | 5.84 |