Combinatorial interpretation and positivity of Kerov's character polynomials

Abstract : Kerov's polynomials give irreducible character values in term of the free cumulants of the associated Young diagram. We prove in this article a positivity result on their coefficients, which extends a conjecture of S. Kerov. Our method, through decomposition of maps, gives a description of the coefficients of the k-th Kerov's polynomials using permutations in S(k). We also obtain explicit formulas or combinatorial interpretations for some coefficients. In particular, we are able to compute the subdominant term for character values on any fixed permutation (it was known for cycles).
Type de document :
Article dans une revue
Journal of Algebraic Combinatorics / Journal of Algebraic Combinatorics An International Journal, 2009, 29 (4), pp.473-507. 〈10.1007/s10801-008-0147-y〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00418450
Contributeur : Valentin Feray <>
Soumis le : vendredi 18 septembre 2009 - 16:02:53
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

Identifiants

Citation

Valentin Féray. Combinatorial interpretation and positivity of Kerov's character polynomials. Journal of Algebraic Combinatorics / Journal of Algebraic Combinatorics An International Journal, 2009, 29 (4), pp.473-507. 〈10.1007/s10801-008-0147-y〉. 〈hal-00418450〉

Partager

Métriques

Consultations de la notice

266