Cylindric partitions and some new $A_2$ Rogers-Ramanujan identities

TL;DR

This paper explores generating functions for cylindric partitions with specific profiles, leading to the discovery and proof of seven new $A_2$ Rogers-Ramanujan identities modulo 8 involving complex quadruple sums.

Contribution

It introduces seven new $A_2$ Rogers-Ramanujan identities modulo 8 derived from cylindric partition generating functions, expanding the understanding of these identities.

Findings

Seven new $A_2$ Rogers-Ramanujan identities modulo 8

Connections with previous work of Andrews, Schilling, and Warnaar

Use of cylindric partitions with specific profiles

Abstract

We study the generating functions for cylindric partitions with profile $(c_1,c_2,c_3)$ for all $c_1,c_2,c_3$ such that $c_1+c_2+c_3=5$. This allows us to discover and prove seven new $A_2$ Rogers-Ramanujan identities modulo $8$ with quadruple sums, related with work of Andrews, Schilling, and Warnaar.