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

[摘要] We extend recent results of Ono and Raji, relating the number of self-conjugate 7-core partitions to Hurwitz class numbers. Furthermore, we give a combinatorial explanation for the curious equality 2 (sc7)(8n + 1) = c(4)(7n + 2). We also conjecture that an equality of this shape holds if and only if t = 4, proving the cases t epsilon {2, 3, 5} and giving partial results for t > 5. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-01

[关键词] t-core partitions;Hurwitzclass numbers;Abaci and t-residuediagrams