The Littlewood decomposition via colored Frobenius partitions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909655269113856 |
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| author | Cho, Hyunsoo Kim, Eunmi Yee, Ae Ja |
| author_facet | Cho, Hyunsoo Kim, Eunmi Yee, Ae Ja |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Littlewood decomposition via colored Frobenius partitions Cho, Hyunsoo Kim, Eunmi Yee, Ae Ja Combinatorics 05A17, 11P81 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. |
| title | The Littlewood decomposition via colored Frobenius partitions |
| topic | Combinatorics 05A17, 11P81 |
| url | https://arxiv.org/abs/2503.03121 |