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arXiv · 2605.27214

On the cycle structure of the symmetric tensor power of permutations

Sebastian Caballero·Diego Villamizar
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Abstract

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.

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Sebastian Caballero, Diego Villamizar. 2026-05-26. On the cycle structure of the symmetric tensor power of permutations. https://arxiv.org/abs/2605.27214

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