A note on polynomials for character degrees

2025/09/16 by Yuval Roichman, Roichman, Yuval
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Representation Theory (math.RT) #Robotic Mechanisms and Dynamics

paper · pdf · doi:10.48550/arxiv.2509.13190

openalex publication_date 2025/09/16 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

A recent result of Cohen and Zemel provides an elegant expansion of the Rasala polynomials for symmetric group character degrees. In this note we present an alternative short algebraic proof. Extensions to polynomials of character values follow.

Citations

• Polynomial Expressions for the Dimensions of the Representations of Symmetric Groups and Restricted Standard Young Tableaux

Related

• Stanley's character polynomials and coloured factorizations in the symmetric group
• Methods and questions in character degrees of finite groups
• Equal knapsack identities between symmetric group character degrees
• An explicit form for Kerov's character polynomials
• New Identities in the Character Table of Symmetric Groups involving Riordan Numbers