Note on parity and the irreducible characters of the symmetric group

TL;DR

This paper proves a theorem and proposes a conjecture regarding the count of even entries in the symmetric group's character table, contributing to the understanding of its algebraic structure.

Contribution

It introduces a new theorem and conjecture about the distribution of even entries in the symmetric group's character table.

Findings

Proved a specific theorem about character table entries.

Formulated a conjecture on the number of even entries.

Provides insights into the structure of symmetric group characters.

Abstract

The object of this short note is to prove a theorem and present a conjecture for the number of even entries in the character table of the symmetric group.