论文标题
大型$ p $ -core $ p'$ - 分区和在添加剂残留图上行走
Large $p$-core $p'$-partitions and walks on the additive residue graph
论文作者
论文摘要
本文调查了既没有零件，也不挂钩长度除以$ p $的分区，称为$ p $ - core $ p'$ - 分区。我们表明，最大的$ p $ -core $ p'$ - 分区对应于带有顶点$ \ {0，1，\ ldots，p-1 \} $的图表上最长的步行，并通过添加的modulo $ p $定义了标记的边缘。我们还展示了一个大型$ p $ core $ p'$ - 分区的明显家族，其大小的最大分区的大小与麦克斯普里特（McSpirit）和昂诺（Ono）发现的上限相同。
This paper investigates partitions which have neither parts nor hook lengths divisible by $p$, referred to as $p$-core $p'$-partitions. We show that the largest $p$-core $p'$-partition corresponds to the longest walk on a graph with vertices $\{0, 1, \ldots, p-1\}$ and labelled edges defined via addition modulo $p$. We also exhibit an explicit family of large $p$-core $p'$-partitions, giving a lower bound on the size of the largest such partition which is of the same degree as the upper bound found by McSpirit and Ono.
