Geodesic
Combinatorial interpretation and positivity of Kerov's character polynomials
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 4, pp. 473-507.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Kerov's polynomials give irreducible character values in terms 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 polynomial 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).
Keywords: keywords representations, symmetric group, maps 
@article{JAC_2009__29_4_a2,
     author = {F\'eray, Valentin},
     title = {Combinatorial interpretation and positivity of {Kerov's} character polynomials},
     journal = {Journal of Algebraic Combinatorics},
     pages = {473--507},
     publisher = {mathdoc},
     volume = {29},
     number = {4},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2009__29_4_a2/}
}
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Féray, Valentin. Combinatorial interpretation and positivity of Kerov's character polynomials. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 4, pp. 473-507. http://geodesic.mathdoc.fr/item/JAC_2009__29_4_a2/