An explicit formula for the characters of the symmetric group

TL;DR

This paper presents an explicit formula for the normalized characters of the symmetric group, expressing them in terms of the contents of the partition that labels each representation.

Contribution

It provides a new explicit expression for symmetric group characters based on partition contents, advancing algebraic combinatorics.

Findings

Derived an explicit formula for normalized characters

Expressed characters in terms of partition contents

Simplified calculations of symmetric group characters

Abstract

We give an explicit expression of the normalized characters of the symmetric group in terms of the contents of the partition labelling the representation.