Asymptotics of characters of symmetric groups: structure of Kerov character polynomials

Details Asymptotics of characters of symmetric groups: structure of Kerov character polynomials Asymptotics of characters of symmetric groups: structure of Kerov character polynomials

2009-11-05

arxiv.org/abs/0911.1038v2

Journal of Combinatorial Theory, Series A, 119 (6), 2012, pp 1174-1193

Mathematics

Combinatorics

Scientific paper

10.1016/j.jcta.2012.02.008

We study asymptotics of characters of the symmetric groups on a fixed conjugacy class. It was proved by Kerov that such a character can be expressed as a polynomial in free cumulants of the Young diagram (certain functionals describing the shape of the Young diagram). We show that for each genus there exists a universal symmetric polynomial which gives the coefficients of the part of Kerov character polynomials with the prescribed homogeneous degree. The existence of such symmetric polynomials was conjectured by Lassalle.

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