Kerov character多项式的一种显式形式
An explicit form for Kerov's character polynomials
摘要：
Kerov认为归一化字符的不可约表示的对称群，评估一个循环，作为一个多项式的自由累积量。Biane证明了该多项式具有整系数，并作了各种证明。最近，Sniady证明了该多项式中第一类非平凡项的Biane的严格显式。本文给出了Kerov特征多项式中所有项的显式表达式。我们的方法是通过拉格朗日反演。
英文摘要：
Kerov considered the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as a polynomial in free cumulants. Biane has proved that this polynomial has integer coefficients, and made various conjectures. Recently, Sniady has proved Biane's conjectured explicit form for the first family of nontrivial terms in this polynomial. In this paper, we give an explicit expression for all terms in Kerov's character polynomials. Our method is through Lagrange inversion.
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