Two positivity conjectures for Kerov polynomials
Abstract
Description
Kerov 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. Math
15 pages, LaTeX, final version, to appear in Adv. Appl. Math