A remark on Frobenius characters for set representations of symmetric groups

TL;DR

This paper provides a combinatorial interpretation of the coefficients in the Frobenius character expansion for set (permutation) representations of symmetric groups, linking representation theory with symmetric functions.

Contribution

It introduces a novel combinatorial interpretation for Frobenius character coefficients in the context of symmetric group set representations.

Findings

Coefficients are interpretable combinatorially

Links between permutation representations and symmetric functions

Enhances understanding of Frobenius characters in symmetric groups

Abstract

For any set representation (permutation representation) of the symmetric group $S_n$, we give combinatorial interpretation for coefficients of its Frobenius character expanded in the basis of monomial symmetric functions.