On the character tables of symmetric groups

TL;DR

This paper investigates the pattern of zeros and non-zeros in the character tables of symmetric groups, focusing on self-conjugate partitions and their relation to odd permutations.

Contribution

It provides a detailed analysis of zeros in the character tables of symmetric groups, especially for self-conjugate partitions, enhancing understanding of their structure.

Findings

Identifies patterns of zeros in character tables

Analyzes zeros for self-conjugate partitions

Highlights relation to odd permutations

Abstract

In this paper, some zeros and non-zeros in the character tables of symmetric groups are displayed in the partition forms. In particular, more zeros of self conjugate partitions beside odd permutations are heavily investigated.