Two positivity conjectures for Kerov polynomials

Details Two positivity conjectures for Kerov polynomials Two positivity conjectures for Kerov polynomials

2007-10-12

arxiv.org/abs/0710.2454v4

Advances in Applied Mathematics, 41 (2008), 407-422

Mathematics

Combinatorics

15 pages, LaTeX, final version, to appear in Adv. Appl. Math

Scientific paper

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.

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