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

Sylvie Corteel, Jehanne Dousse, Ali K. Uncu

Published 2020-11-25Version 1

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.