Discrete Mathematics and Optimization Seminar

Monday November 10th at 4.30pm
Burnside 1205

Title. Questions of Schur-Positivity.

Abstract. Schur functions, which we will define combinatorially, are symmetric functions that form a basis for the ring of symmetric functions.
A symmetric function is said to be Schur-positive if, when expanded as a linear combination of Schur functions, all the coefficients are
positive. Perhaps the most famous example of a Schur-positive function is the product of any pair of Schur functions.
We will address the following question: when is the difference of two of these products of pairs Schur-positive?

Our approach will be combinatorial and we will discuss, in particular, recent conjectures of Fomin, Fulton, Li and Poon.
The emphasis will be on introducing the concepts and conjectures, rather than on technical results.