The range of repetition in reduced decompositions

2020/02/24 by Tenner, Bridget Eileen
#05E15 #Combinatorics (math.CO) #FOS: Mathematics #Primary: 05A05 #Secondary: 05A19

paper · doi:10.48550/arxiv.2002.10503

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.

Related

• Repetition in reduced decompositions
• On the expected number of commutations in reduced words
• Increasing and Decreasing Subsequences of Permutations and Their Variants
• On Graphs of Sets of Reduced Words
• On the Best Upper Bound for Permutations Avoiding A Pattern of a Given Length