论文标题
在$ t $ - 核和自变轭$（2T-1）$ - 算术进度中的核心分区
On $t$-core and self-conjugate $(2t-1)$-core partitions in arithmetic progressions
论文作者
论文摘要
我们将Ono和Raji的最新结果扩展到了Hurwitz的班级编号，将自变$ 7 $的分区的数量联系起来。此外，我们给出了一个好奇的平等的组合解释$ 2 \ permatatorName {sc} _7（8n+1）= \ operatatorName {c} _4（7n+2）$。我们还猜想，这种形状的平等性在且仅当$ t = 4 $时，证明了$ t \ in \ {2,3,5 \} $，并以$ t> 5 $给出部分结果。
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 $2\operatorname{sc}_7(8n+1) = \operatorname{c}_4(7n+2)$. We also conjecture that an equality of this shape holds if and only if $t=4$, proving the cases $t\in\{2,3,5\}$ and giving partial results for $t>5$.
