Large-scale Monte Carlo simulations for zeros in character tables of symmetric groups

TL;DR

This paper reports large-scale Monte Carlo simulations indicating that nearly all zeros in the character tables of large symmetric groups are of a classical type, challenging prior assumptions about their distribution.

Contribution

It provides extensive computational evidence that most zeros are classical, overturning previous beliefs about the prevalence of non-classical zeros in large symmetric groups.

Findings

Almost all zeros are of a single classical type

Simulations surpass previous computational efforts

Results challenge earlier conjectures about zero distribution

Abstract

This is a brief report on some recent large-scale Monte Carlo simulations for approximating the density of zeros in character tables of large symmetric groups. Previous computations suggested that a large fraction of zeros cannot be explained by classical vanishing results. Our computations eclipse previous ones and suggest that the opposite is true. We find empirically that almost all of the zeros are of a single classical type.