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arXiv · 2410.04644

A New Symmetric Function Identity With an Application to symmetric group character values

Karlee J. Westrem
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Abstract

Symmetric functions show up in several areas of mathematics including enumerative combinatorics and representation theory. Tewodros Amdeberhan conjectures equalities of $Σ_n$ characters sums over a new set called $Ev(λ)$. When investigating the alternating sum of characters for $Ev(λ)$ written in terms of the inner product of Schur functions and power sum symmetric functions, we found an equality between the alternating sum of power sum symmetric polynomials and a product of monomial symmetric polynomials. As a consequence, a special case of an alternating sum of $Σ_n$ characters over the set $Ev(λ)$ equals $0$.

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Karlee J. Westrem. 2024-10-06. A New Symmetric Function Identity With an Application to symmetric group character values. https://arxiv.org/abs/2410.04644

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