Cylindric partitions and some new A₂ Rogers-Ramanujan identities

2020/11/25 by Corteel, Sylvie, Dousse, Jehanne, Uncu, Ali K. · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.12828

Abstract

We study the generating functions for cylindric partitions with profile (c₁,c₂,c₃) for all c₁,c₂,c₃ such that c₁+c₂+c₃=5. This allows us to discover and prove seven new A₂ Rogers-Ramanujan identities modulo 8 with quadruple sums, related with work of Andrews, Schilling, and Warnaar.

Cited by

• Tight cylindric partitions
• Method of Weighted Words on Cylindric Partitions

Related

• The A₂ Rogers-Ramanujan identities revisited
• Proofs of Modulo 11 and 13 Cylindric Kanade-Russell Conjectures for A₂ Rogers-Ramanujan Type Identities
• Linked partition ideals and a family of quadruple summations
• A MacMahon Analysis View of Cylindric Partitions
• Partition identities associated to Rogers-Ramanujan type identities