Signed Counting on Restricted Partitions and Combinatorial Proofs of Three Identities

Abstract

Signed enumerations of l-regular partitions by the parity of the number of parts are known to correspond to partitions with congruence conditions. Inspired by the recent combinatorial approaches of Ballantine-Merca and Liu for such identities, we provide combinatorial proofs of three identities for l-regular partitions and their variants. Two of these were originally established analytically by Hickerson and Robbins, respectively.

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