Schur positivity via pattern avoidance
Characterizing sets of permutations whose associated quasi-symmetric function is symmetric and Schur-positive is a long-standing problem in algebraic combinatorics. We will explain the significance of the problem and describe recent progress.
A general method to construct Schur-positive sets and multisets, based on pattern avoidance and geometric grids will be presented. This approach produces many new instances of Schur-positive sets, and provides a broad framework that explains the existence of known such sets that until now were sporadic cases.
Joint with Sergi Elizalde.