English

On self-conjugate $(s, s+1,\ldots, s+k)$-core partitions

Combinatorics 2019-05-03 v1

Abstract

Simultaneous core partitions have been widely studied since Anderson's work on the enumeration of (s,t)(s,t)-core partitions. Amdeberhan and Leven showed that the number of (s,s+1,,s+k)(s,s+1, \ldots, s+k)-core partitions is equal to the number of (s,k)(s, k)-Dyck paths. In this paper, we prove that self-conjugate (s,s+1,,s+k)(s,s+1, \ldots, s+k)-core partitions are equinumerous with symmetric (s,k)(s, k)-Dyck paths, confirming a conjecture posed by Cho, Huh and Sohn.

Keywords

Cite

@article{arxiv.1905.00570,
  title  = {On self-conjugate $(s, s+1,\ldots, s+k)$-core partitions},
  author = {Sherry H. F. Yan and Yao Yu and Hao Zhou},
  journal= {arXiv preprint arXiv:1905.00570},
  year   = {2019}
}
R2 v1 2026-06-23T08:54:50.230Z