A conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group

TL;DR

This paper proposes a conjectural generalization of a known formula for symmetric group character values from rectangular to arbitrary shapes, aiming to deepen combinatorial understanding of these characters.

Contribution

It introduces a conjectured combinatorial interpretation extending a specific character value formula to all partition shapes.

Findings

Proposes a conjectural formula for arbitrary shapes

Extends previous rectangular shape results

Provides a new perspective on symmetric group characters

Abstract

In math.CO/0109093 the author obtained a formula for the value of an irreducible symmetric group character indexed by a partition of rectangular shape. In the present paper this formula is (conjecturally) generalized to arbitrary shapes.