2609.02888 STRUCTURAL PROGRESS ON OPAC-038: SIGN FILTERS, BINARY COMPRESSION, SPLIT FUSION, AND COMPLEMENTARY MINORS
For an irreducible character χλ of the symmetric group Sn, let Nn−(λ) = #{µ ⊢ n : χλ(µ) < 0}, with conjugacy classes counted uniformly. OPAC-038 asks whether, for all sufficiently large n, this statistic is maximized by the sign representation.