论文标题
给定的$ S $核和$ t $ core的最小分区
Minimal partitions with a given $s$-core and $t$-core
论文作者
论文摘要
假设$ s $和$ t $是coprime正整数，让$σ$为$ s $ core分区和$τ$ a $ t $ core分区。在本文中，我们考虑了$ n $的$ n $的$ \ Mathcal p_ {σ，τ}（n）$，带有$ s $ -core $σ$和$ t $ -core $τ$。 We find the smallest $n$ for which this set is non-empty, and show that for this value of $n$ the partitions in $\mathcal P_{σ,τ}(n)$ (which we call $(σ,τ)$-minimal partitions) are in bijection with a certain class of $(0,1)$-matrices with $s$ rows and $t$ columns. 然后，我们使用这些结果来考虑共轭分区：我们确切确定何时$ \ MATHCAL P_ {σ，τ}（n）$由一对分区组成，何时$ \ Mathcal P_ {σ，τ，τ}（n）$包含一个独特的自我juggate分区。
Suppose $s$ and $t$ are coprime positive integers, and let $σ$ be an $s$-core partition and $τ$ a $t$-core partition. In this paper we consider the set $\mathcal P_{σ,τ}(n)$ of partitions of $n$ with $s$-core $σ$ and $t$-core $τ$. We find the smallest $n$ for which this set is non-empty, and show that for this value of $n$ the partitions in $\mathcal P_{σ,τ}(n)$ (which we call $(σ,τ)$-minimal partitions) are in bijection with a certain class of $(0,1)$-matrices with $s$ rows and $t$ columns. We then use these results in considering conjugate partitions: we determine exactly when the set $\mathcal P_{σ,τ}(n)$ consists of a conjugate pair of partitions, and when $\mathcal P_{σ,τ}(n)$ contains a unique self-conjugate partition.
