Overpartitions, lattice paths, and Rogers-Ramanujan identities

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:114

Article

Corteel, Sylvie ; Mallet, Olivier

关键词: partitions;    overpartitions;    Rogers-Ramanujan identities;    lattice paths;   

DOI  :  10.1016/j.jcta.2007.02.004

来源: Elsevier

【 摘 要 】

We extend partition-theoretic work of Andrews, Bressoud, and Burge to overpartitions, defining the notions of successive ranks, generalized Durfee squares, and generalized lattice paths, and then relating these to overpartitions defined by multiplicity conditions on the parts. This leads to many new partition and overpartition identities, and provides a unification of a number of well-known identities of the Rogers-Ramanujan type. Among these are Gordon's generalization of the Rogers-Ramanujan identities, Andrews' generalization of the Gollnitz-Gordon identities, and Lovejoy's Gordon's theorems for overpartitions. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free