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

Published 25 Nov 2020 in math.CO | (2011.12828v1)

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.

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