Part bounds for the Sylow permutation characters of $S_n$

Lorenzo Vanzi

Part bounds for the Sylow permutation characters of $S_n$

Representation Theory 2026-07-02 v1 Combinatorics Group Theory

Authors: Lorenzo Vanzi

Abstract

We study the Sylow permutation character of the symmetric group at the prime 2 and prove some new bounds on the number of parts of partitions corresponding to its constituents.

Keywords

Sylow permutation character symmetric group partitions character theory

Cite

@article{arxiv.2607.02433,
  title  = {Part bounds for the Sylow permutation characters of $S_n$},
  author = {Lorenzo Vanzi},
  journal= {arXiv preprint arXiv:2607.02433},
  year   = {2026}
}