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math.CO2007
Two positivity conjectures for Kerov polynomials
Michel Lassalle
Kerov polynomials express the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as polynomials in the free cumulants of the associa…
math.CO2007
An explicit formula for the characters of the symmetric group
Michel Lassalle
We give an explicit expression of the normalized characters of the symmetric group in terms of the contents of the partition labelling the representation.
math.CO2007
A positivity conjecture for Jack polynomials
Michel Lassalle
We present a positivity conjecture for the coefficients of the development of Jack polynomials in terms of power sums. This extends Stanley's ex-conjecture about normalized charact…