Combinatorial proofs for partitions with repeated smallest part

2025/05/08 by Chen, Dandan, Chen, Rong, Zhao, Mengjie
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.05079

Abstract

Recently, Andrews and El Bachraoui considered the number of integer partitions whose smallest part is repeated exactly k times and the remaining parts are not repeated. They presented several interesting results and posed questions regarding combinatorial proofs for these identities. In this paper, we establish bijections to provide combinatorial proofs for these results.

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