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

2024/10/06 by Karlee J. Westrem, Westrem, Karlee J. · 1 citation
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Matrix Theory and Algorithms #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2410.04644

openalex publication_date 2024/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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