Overpartitions, lattice paths and Rogers-Ramanujan identities

Abstract

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 Göllnitz-Gordon identities, and Lovejoy's ``Gordon's theorems for overpartitions."

Cited by in corpus (8)

• M_2-rank differences for partitions without repeated odd parts
• Rank differences for overpartitions
• IdentityFinder and some new identities of Rogers-Ramanujan type
• Homogeneous components in the moduli space of sheaves and Virasoro characters
• A Rademacher Type Formula For Partitions and Overpartitions
• An Overpartition Analogue of Bressoud's Theorem of Rogers-Ramanujan Type
• The Bressoud-Göllnitz-Gordon Theorem for Overpartitions of even moduli
• Anti-lecture Hall Compositions and Overpartitions