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Combinatorial interpretation and positivity of Kerov's character polynomials

Abstract : 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.
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Valentin Féray. Combinatorial interpretation and positivity of Kerov's character polynomials. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.93-104, ⟨10.46298/dmtcs.3629⟩. ⟨hal-01185164⟩

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