Séminaire Lotharingien de Combinatoire, B69c (2013), 40 pp.

Tom Denton

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.

Received: June 18, 2012. Revised: June 10, 2013. Accepted: June 10, 2013.

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