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 -core partitions to Hurwitz class numbers. Furthermore, we give a combinatorial explanation for the curious equality . We also conjecture that an equality of this shape holds if and only if , proving the cases and giving partial results for .
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}
}