On the cycle structure of the symmetric tensor power of permutations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910261130035200 |
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| author | Caballero, Sebastian Villamizar, Diego |
| author_facet | Caballero, Sebastian Villamizar, Diego |
| contents | Problem 8.1 in Astaiza et. al. asks about the relationship between the cycle decomposition of a permutation $σ$ and that of its symmetric tensor power $σ^{\odot k}$. In this paper, we investigate this question and give formulas for computing the number of fixed points and, in the case of a permutation containing at most one cycle of length greater than one, the number of $s$-cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27214 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the cycle structure of the symmetric tensor power of permutations Caballero, Sebastian Villamizar, Diego Combinatorics 05A15 Problem 8.1 in Astaiza et. al. asks about the relationship between the cycle decomposition of a permutation $σ$ and that of its symmetric tensor power $σ^{\odot k}$. In this paper, we investigate this question and give formulas for computing the number of fixed points and, in the case of a permutation containing at most one cycle of length greater than one, the number of $s$-cycles. |
| title | On the cycle structure of the symmetric tensor power of permutations |
| topic | Combinatorics 05A15 |
| url | https://arxiv.org/abs/2605.27214 |