Kerov character多项式的组合解释及其正性
Combinatorial interpretation and positivity of Kerov's character polynomials
摘要：
Kerov多项式给出了不可约特征值的自由累积量的相关的杨图。本文证明了它们的系数的一个正性结果，推广了S.凯洛夫我们的方法，通过分解的地图，给出了一个描述的系数的第k次Kerov多项式使用置换在S（k）。我们还获得了一些系数的显式公式或组合解释。特别是，我们能够计算任何固定排列上字符值的次显性项（这是已知的循环）。
英文摘要：
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).
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