Simon Watts

EXTREMAL NEGATIVITY IN SYMMETRIC-GROUP CHARACTER TABLES: PARITY GEOMETRY, SUPPORT BARRIERS, AND CRITICAL JUCYS-WEINGARTEN DUALITY

This preprint investigates an open problem in algebraic combinatorics: determining whether the sign representation of the symmetric group \(S_n\) maximizes the number of negative entries in its irreducible character row. The paper develops a comprehensive framework combining stru...

EXTREMAL NEGATIVITY IN SYMMETRIC-GROUP CHARACTER TABLES: PARITY GEOMETRY, SUPPORT BARRIERS, AND CRITICAL JUCYS-WEINGARTEN DUALITY

This preprint investigates an open problem in algebraic combinatorics: determining whether the sign representation of the symmetric group \(S_n\) maximizes the number of negative entries in its irreducible character row. The paper develops a comprehensive framework combining stru...