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 $2{\mathrm{sc}}_7(8n+1)={\mathrm{c}}_4(7n+2)$. We also conjecture that an equality of this shape holds if and only if $t=4$, proving the cases $t\in \{2,3,5\}$ and giving partial results for $t>5$.

中文翻译：

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上吨-core和自共轭（2吨 - 1）的算术级数-core分区

我们扩展了Ono和Raji的最新结果，将自共轭7核分区的数量与Hurwitz类编号相关联。此外，我们对好奇的平等给出了组合的解释$\mathrm{2个}{\mathrm{SC}}_7（8ñ+\mathrm{1个}）={\mathrm{C}}_4（7ñ+\mathrm{2个}）$。我们还推测，当且仅当这种形状的等式成立$Ť=4$，证明案件 $Ť\in \{\mathrm{2个}，3，5\}$ 并给出部分结果 $Ť>5$。