Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations

By Maciej Dolkega, Valentin F'eray, Piotr Śniady. 2008

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Abstract We find an explicit combinatorial interpretation of the coefficients of Kerov character polynomials which express the value of normalized irreducible characters of the symmetric groups S ( n ) in terms of free cumulants R 2 , R 3 , … of the corresponding Young diagram. Our interpretation is based on counting certain factorizations of a given permutation.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fbcfd5770ac02e27f6171bf1ed65109f7dcf4c6c

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