Two new partition identities are proved: three-colored partitions with certain forbidden differences have generating functions equal to a distinct-parts factor times the first or second Rogers-Ramanujan product.
Tight cylindric partitions
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abstract
In this note, we initiate the study of generating functions for tight cylindric partitions. For general (i.e., $r$-rowed for $r\geq 2$) tight cylindric partitions, we provide analogs of the Corteel--Welsh functional equations. We prove closed forms for the bivariate generating functions for 2-rowed tight cylindric partitions. We also show that these partitions are in bijection with a class of partitions studied by Dousse, Hardiman, and Konan.
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On a pair of three-colored (mod 10) partition identities
Two new partition identities are proved: three-colored partitions with certain forbidden differences have generating functions equal to a distinct-parts factor times the first or second Rogers-Ramanujan product.