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arXiv:1303.3767 [math.CO]AbstractReferencesReviewsResources

Algebraic and Affine Pattern Avoidance

Tom Denton

Published 2013-03-15Version 1

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.

Comments: Modified from a chapter of the author's dissertation, currently submitted for review for publication
Journal: S\'eminaire Lotharingien de Combinatoire, B69c (2013), 40 pp
Categories: math.CO
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