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arXiv · 2503.03121

The Littlewood decomposition via colored Frobenius partitions

Hyunsoo Cho·Eunmi Kim·Ae Ja Yee
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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.

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Hyunsoo Cho, Eunmi Kim, Ae Ja Yee. 2025-06-21. The Littlewood decomposition via colored Frobenius partitions. https://arxiv.org/abs/2503.03121

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