Algebraic and Topological Combinatorics

Special Session at the Fall Eastern Section Meeting
of the American Mathematical Society

Williams College, Williamstown, MA
October 13-14, 2001

Thomas Braden
(University of Massachusetts, Amherst)

Lower bounds for Kazhdan-Lusztig polynomials from patterns

Abstract [ps] [pdf]: If $x$ and $y$ are elements of a Weyl group $W$, and $W'$ is a subgroup of $W$ generated by reflections, we give lower bounds for $P_{x,w}(1)$ in terms of the cosets containing $x$ and $w$ and their positions within those cosets. If $W = S_n$ this relates to pattern avoidance -- e.g. we get $P_{1,w}(1) \ge P_{1,y}(1)$ where $y$ is any pattern contained in $w$.

This is joint work with Sara Billey.

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last updated: August 21, 2001