On the cycle structure of the symmetric tensor power of permutations

Sebastian Caballero; Diego Villamizar

On the cycle structure of the symmetric tensor power of permutations

Combinatorics 2026-05-27 v1

Authors: Sebastian Caballero , Diego Villamizar

Abstract

Problem 8.1 in Astaiza et. al. asks about the relationship between the cycle decomposition of a permutation $\sigma$ and that of its symmetric tensor power $\sigma ^{\odot k}$ . 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.

Keywords

permutation symmetric tensor power cycle structure fixed points cycle decomposition Astaiza problem

Cite

@article{arxiv.2605.27214,
  title  = {On the cycle structure of the symmetric tensor power of permutations},
  author = {Sebastian Caballero and Diego Villamizar},
  journal= {arXiv preprint arXiv:2605.27214},
  year   = {2026}
}

Comments

13 pages. Presented at SEICCGTC 2026. Submitted to Proceedings

On the cycle structure of the symmetric tensor power of permutations

Abstract

Keywords

Cite

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