2025/03/05 by Hyunsoo Cho, Cho, Hyunsoo, Eunmi Kim +3
Mathematics · #05A17 #11P81 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2503.03121
openalex publication_date 2025/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.