2609.02877 Polynomial-Time Islands for Squared Characters of the Symmetric Group
Ikenmeyer, Pak, and Panova proved that vanishing of an irreducible character chi^lambda(pi) of S_n is C_=P-complete, positivity is PP-complete, and that the pointwise square chi^2 lies in #P only if PH collapses to Sigma_2^p. This note does not alter those theorems.