Two positivity conjectures for Kerov polynomials
Combinatorics
2008-09-07 v4 Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0710.2454,
title = {Two positivity conjectures for Kerov polynomials},
author = {Michel Lassalle},
journal= {arXiv preprint arXiv:0710.2454},
year = {2008}
}
Comments
15 pages, LaTeX, final version, to appear in Adv. Appl. Math