Simon Watts

OPAC-038: Extremal Negativity in Symmetric-Group Character Tables

This preprint studies OPAC-038, the open problem asking whether, for all sufficiently large (n), the sign representation of the symmetric group (S_n) maximizes the number of negative entries among irreducible character-table rows. The paper develops a collection of exact reductio...

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...