Geodesic
Combinatorial interpretation and positivity of Kerov's character polynomials
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008).

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Kerov's polynomials give irreducible character values of the symmetric group in term of the free cumulants of the associated Young diagram. Using a combinatorial approach with maps, we prove in this article a positivity result on their coefficients, which extends a conjecture of S. Kerov. 
@article{DMTCS_2008_special_255_a37,
     author = {F\'eray, Valentin},
     title = {Combinatorial interpretation and positivity of {Kerov's} character polynomials},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)},
     year = {2008},
     doi = {10.46298/dmtcs.3629},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3629/}
}
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Féray, Valentin. Combinatorial interpretation and positivity of Kerov's character polynomials. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) (2008). doi : 10.46298/dmtcs.3629. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3629/

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