2609.02885 PROGRESS ON OPAC-038: BINARY COMPRESSION, SPLIT FUSION, AND UNWEIGHTED CHARACTER INEQUALITIES
For an irreducible character χλ of Sn, let Nn−(λ) be the number of conjugacy classes on which χλ is negative, with no class-size weighting. Hopkins’ OPAC-038 asks whether, for all sufficiently large n, the sign representation maximizes Nn−.