Overpartition pairs and two classes of basic hypergeometric series

Details Overpartition pairs and two classes of basic hypergeometric series Overpartition pairs and two classes of basic hypergeometric series

2007-09-11

arxiv.org/abs/0709.1565v1

Mathematics

Combinatorics

31 pages, To appear in Adv. Math

Scientific paper

We study the combinatorics of two classes of basic hypergeometric series. We first show that these series are the generating functions for certain overpartition pairs defined by frequency conditions on the parts. We then show that when specialized these series are also the generating functions for overpartition pairs with bounded successive ranks, overpartition pairs with conditions on their Durfee dissection, as well as certain lattice paths. When further specialized, the series become infinite products, leading to numerous identities for partitions, overpartitions, and overpartition pairs.

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