Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations

Details Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations

2008-10-17

arxiv.org/abs/0810.3209v3

Adv. Math. 225 (2010), no. 1, 81-120

Mathematics

Combinatorics

Scientific paper

10.1016/j.aim.2010.02.011

We find an explicit combinatorial interpretation of the coefficients of Kerov
character polynomials which express the value of normalized irreducible
characters of the symmetric groups S(n) in terms of free cumulants R_2,R_3,...
of the corresponding Young diagram. Our interpretation is based on counting
certain factorizations of a given permutation.

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