Combinatorial proofs for partitions with repeated smallest part
Combinatorics
2025-05-15 v2 Number Theory
Abstract
Recently, Andrews and El Bachraoui considered the number of integer partitions whose smallest part is repeated exactly 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.
Cite
@article{arxiv.2505.05079,
title = {Combinatorial proofs for partitions with repeated smallest part},
author = {Dandan Chen and Rong Chen and Mengjie Zhao},
journal= {arXiv preprint arXiv:2505.05079},
year = {2025}
}