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

Maciej Dolega , Valentin Féray (1, 2) , Piotr Sniady

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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.

Domaines: Combinatoire [math.CO]; Théorie des représentations [math.RT]

Maciej Dolega, Valentin Féray, Piotr Sniady. Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations. Advances in Mathematics, 2010, 225 (1), pp.81-120. ⟨10.1016/j.aim.2010.02.011⟩. ⟨hal-00418456⟩