Zeros in the character table of the symmetric group

TL;DR

This paper proves a conjecture about the nature of zeros in the character table of the symmetric group, building on computational observations and addressing related questions in algebraic combinatorics.

Contribution

It resolves a conjecture about the special type of zeros in the symmetric group's character table and addresses a related question posed by Stanley.

Findings

Confirmed that most zeros are of a specific special type.

Resolved a conjecture regarding zeros in the character table.

Addressed a related open question by Stanley.

Abstract

Computations of Miller and Scheinerman suggest that the vast majority of the zeros appearing in the character table of the symmetric group are of a certain special type. While we cannot prove this, we resolve a conjecture arising in their paper concerning these zeros, and address a related question of Stanley.