An explicit form for Kerov's character polynomials

Details An explicit form for Kerov's character polynomials An explicit form for Kerov's character polynomials

2005-05-15

arxiv.org/abs/math/0505317v1

Mathematics

Combinatorics

17 pages, 1 figure

Scientific paper

Kerov considered the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as a polynomial in free cumulants. Biane has proved that this polynomial has integer coefficients, and made various conjectures. Recently, Sniady has proved Biane's conjectured explicit form for the first family of nontrivial terms in this polynomial. In this paper, we give an explicit expression for all terms in Kerov's character polynomials. Our method is through Lagrange inversion.

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