The range of repetition in reduced decompositions
Combinatorics
2020-09-09 v2
Abstract
Given a permutation w, we look at the range of how often a simple reflection s_k appears in reduced decompositions of w. We compute the minimum and give a sharp upper bound on the maximum. That bound is in terms of 321- and 3412-patterns in w, specifically as they relate in value and position to k. We also characterize when that minimum and maximum are equal, refining a previous result that braid moves are equivalent to 321-patterns.
Keywords
Cite
@article{arxiv.2002.10503,
title = {The range of repetition in reduced decompositions},
author = {Bridget Eileen Tenner},
journal= {arXiv preprint arXiv:2002.10503},
year = {2020}
}
Comments
corrected Theorem 5.1; to appear in Advances in Applied Mathematics