Divisibility of character values of the symmetric group by prime powers

Peluse, Sarah; Soundararajan, Kannan

doi:10.2140/ant.2025.19.365

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Divisibility of character values of the symmetric group by prime powers

Sarah Peluse and Kannan Soundararajan

Vol. 19 (2025), No. 2, 365–382

DOI: 10.2140/ant.2025.19.365

Abstract

Let $k$ be a positive integer. We show that, as $n$ goes to infinity, almost every entry of the character table of $S_{n}$ is divisible by $k$ . This proves a conjecture of Miller.

Keywords

character table, symmetric group, divisibility

Mathematical Subject Classification

Primary: 05A17, 20C30

Milestones

Received: 7 January 2023

Revised: 29 January 2024

Accepted: 5 March 2024

Published: 31 January 2025

Authors

Sarah Peluse
Department of Mathematics Stanford University Stanford, CA United States

Kannan Soundararajan
Department of Mathematics Stanford University Stanford, CA United States

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Vol. 19, No. 2, 2025