Permutation patterns and Stanley symmetric functionsAlgebra & Discrete Mathematics
|Speaker:||Brendan Pawlowski, Univ. of Washington|
|Start time:||Mon, Apr 28 2014, 12:10PM|
Given a permutation w, Stanley defined a symmetric function F_w which encodes information about the reduced words of w, and showed that F_w is a single Schur function exactly when w avoids the pattern 2143. I will give a more general sense in which the Schur expansion of F_w respects pattern containment; in particular, the number of Schur function terms is determined by pattern avoidance conditions on w. If time permits I will discuss how this work relates to the computation of cohomology classes of certain subvarieties of Grassmannians, resolving some cases of a conjecture of Liu. This is joint work with Sara Billey.