Bruhat-restricted pattern avoidance

Alexander Woo, UC Davis

A large permutation $w$ (thought of as a sequence of numbers) is said to avoid a smaller permutation $v$ if $w$ does not a subsequence in the relative order given by $v$. This notion has been the subject of a large amount of recent work, most notably around the Stanley-Wilf conjecture (now proven) about how many such permutations there are asymptotically. Inspired by some geometry, we introduce a generalization of pattern avoidance, discuss some of its basic properties, and pose some questions. This talk will be based on joint work with Alexander Yong.