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Permutation patterns and Stanley symmetric functions

Algebra & Discrete Mathematics

Speaker: Brendan Pawlowski, Univ. of Washington
Location: 2112 MSB
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.