The Littlewood decomposition via colored Frobenius partitions

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.