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

الأصل · EN

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 R₂,R₃,... of the corresponding Young diagram. Our interpretation is based on counting certain factorizations of a given permutation.