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

Dandan Chen; Ziyin Zou

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arXiv · 2410.14126

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

Dandan Chen·Ziyin Zou

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Abstract

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.

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Dandan Chen, Ziyin Zou. 2025-08-29. Combinatorial proof of identities involving partitions with distinct even parts and 4-regular partitions. https://arxiv.org/abs/2410.14126

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