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

2023/10/11 by Alexander R. Miller, Miller, Alexander R., Danny Scheinerman +1
Mathematics · Physics and Astronomy · #20C30 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Group Theory (math.GR) #Markov Chains and Monte Carlo Methods #Number Theory (math.NT) #Representation Theory (math.RT) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2310.07500

openalex publication_date 2023/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• On the character tables of symmetric groups
• Groups with a small average number of zeros in the character table
• The sparsity of character tables of high rank groups of Lie type
• Lower Bound for The Number of Zeros in The Character Table of The Symmetric Group
• The probability that a character value is zero for the symmetric group