Kerov's character polynomials and permutations
| Speaker: | Ian Goulden |
|---|---|
| Affiliation: | University of Waterloo |
| Room: | Mathematics & Computer Building (MC) 5158 |
Abstract:
Kerov's character polynomials give an expression for a particular scaling of irreducible characters of the symmetric group, as a polynomial in the free cumulants of the corresponding Young diagram. These polynomials are particularly convenient for determining asymptotics of the corresponding characters. The coefficients have long been known to be integers, and conjectured to be positive. A recent proof of this positivity has recently been announced by Dolega, Feray and Sniady, in which they identify the coefficients combinatorially, as the number of permutations subject to specified properties. This talk is intended to be expository, providing the necessary background to understand the combinatorial significance of characters, free cumulants and these polynomials.