Inequalities for full rank differences of 2-marked Durfee symbols

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:119

Article

Bringmann, Kathrin¹  Kane, Ben¹ 

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

关键词: k-Marked Durfee symbols;    Rank;    Partitions;    Ramanujan;    Congruences;   

DOI  :  10.1016/j.jcta.2011.10.003

来源: Elsevier

【 摘 要 】

In this paper, we obtain infinitely many non-trivial identities and inequalities between full rank differences for 2-marked Durfee symbols, a generalization of partitions introduced by Andrews. A certain strict inequality, which almost always holds, shows that identities for Dyson's rank, similar to those proven by Atkin and Swinnerton-Dyer, are quite rare. By showing an analogous strict inequality, we show that such non-trivial identities are also rare for the full rank, but on the other hand we obtain an infinite family of non-trivial identities, in contrast with the partition theoretic case. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free