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