English

On $t$-core and self-conjugate $(2t-1)$-core partitions in arithmetic progressions

Number Theory 2021-02-16 v3 Combinatorics

Abstract

We extend recent results of Ono and Raji, relating the number of self-conjugate 77-core partitions to Hurwitz class numbers. Furthermore, we give a combinatorial explanation for the curious equality 2sc7(8n+1)=c4(7n+2)2\operatorname{sc}_7(8n+1) = \operatorname{c}_4(7n+2). We also conjecture that an equality of this shape holds if and only if t=4t=4, proving the cases t{2,3,5}t\in\{2,3,5\} and giving partial results for t>5t>5.

Keywords

Cite

@article{arxiv.2005.07020,
  title  = {On $t$-core and self-conjugate $(2t-1)$-core partitions in arithmetic progressions},
  author = {Kathrin Bringmann and Ben Kane and Joshua Males},
  journal= {arXiv preprint arXiv:2005.07020},
  year   = {2021}
}
R2 v1 2026-06-23T15:32:58.129Z