Combinatorial proof of identities involving partitions with distinct even parts and 4-regular partitions

Dandan Chen, Ziyin Zou

Published 2024-10-18Version 1

Recently Andrews and Bachraoui proved identities relating certain restricted partitions into distinct even parts with restricted 4-regular partitions by the theory of basic hypergeometric series. They also posed a question regarding combinatorial proofs for these results. In this paper, we establish bijections to provide combinatorial proofs for these results.