2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168430Kerov polynomials express the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as polynomials in the free cumulants of the associated Young diagram. We present two positivity conjectures for their coefficients. The latter are stronger than the positivity conjecture of Kerov-Biane, recently proved by Feray.15 pages, LaTeX, final version, to appear in Adv. Appl. MathCombinatoricsRepresentation Theorytext