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

Abstract

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 2sc7(8n+1)=c4(7n+2). We also conjecture that an equality of this shape holds if and only if t=4, proving the cases t∈{2,3,5} and giving partial results for t>5.