Algebraic and Affine Pattern Avoidance
Combinatorics
2013-08-06 v1
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.
Cite
@article{arxiv.1303.3767,
title = {Algebraic and Affine Pattern Avoidance},
author = {Tom Denton},
journal= {arXiv preprint arXiv:1303.3767},
year = {2013}
}
Comments
Modified from a chapter of the author's dissertation, currently submitted for review for publication