Abstract: Enumerating permutations that avoid a given list of patterns is a central problem in algebraic combinatorics. Back in the '90s, Mark Haiman calculated the generating function
for permutations avoiding the smooth patterns 4231 and 3412 by studying the fiber bundle structures of Schubert varieties. In this talk, I will discuss joint work with William Slofstra where we use similar ideas to enumerate affine permutations that avoid these same patterns.
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