Algebraic and Affine Pattern Avoidance

Abstract

We investigate various connections between the 0-Hecke monoid, Catalan monoid, and pattern avoidance in permutations, providing new tools for approaching pattern avoidance in an algebraic framework. In particular, we characterize containment of a class of `long' patterns as equivalent to the existence of a corresponding factorization. We then generalize some of our constructions to the affine setting.

Modified from a chapter of the author's dissertation, currently submitted for review for publication