English

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 kk 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.

Keywords

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}
}
R2 v1 2026-06-28T23:25:32.122Z