Title: The Littlewood decomposition via colored Frobenius partitions Show Chinese title

Title: 通过彩色弗罗贝尼乌斯分拆的利特尔伍德分解

Abstract: The Littlewood decomposition for partitions is a well-known bijection between partitions and pairs of $t$-core and $t$-quotient partitions. This decomposition can be described in several ways, such as the $t$-abacus method of James or the biinfinite word method of Garvan, Kim, and Stanton. In a recent study, Frobenius partitions have proven to be a highly useful tool in dealing with partition statistics related to $t$-core partitions. Motivated by this study, in this paper, we present an alternative description of the Littlewood decomposition using Frobenius partitions. We also apply our approach to self-conjugate partitions and doubled distinct partitions, and give new characterizations of their $t$-cores and $t$-quotients. Show Chinese abstract

Abstract: 分拆的Littlewood分解是分拆与一对$t$-核心分拆和$t$-商分拆之间的著名双射。 这种分解可以用多种方式描述，例如James的$t$-算盘方法或Garvan、Kim和Stanton的双无限单词方法。 在最近的研究中，Frobenius分拆已被证明是在处理与$t$-核心分拆相关的分拆统计量时非常有用的工具。 受此研究的启发，本文我们提出了一种使用Frobenius分拆来描述Littlewood分解的替代方法。 我们还将我们的方法应用于自共轭分拆和加倍不同分拆，并给出了它们的$t$-核心和$t$-商的新特征。