2608.02868 EXTREMAL NEGATIVITY IN SYMMETRIC-GROUP CHARACTER TABLES: SOLVED SECTORS AND AN ARITHMETIC SQUARE-CORE REDUCTION
For an irreducible character χλ of Sn, let Nn−(λ) = #{µ ⊢ n : χλ(µ) < 0}, with one entry counted for each conjugacy class. OPAC-038 asks whether the sign representation eventually maximizes Nn−.