Disarray, reduced words, and 321-avoidance in George groups

2024/04/09 by Joel Brewster Lewis, Lewis, Joel Brewster, Bridget Eileen Tenner +1 · 1 citation
Computer Science · Mathematics · #semigroups and automata theory #Finite Group Theory Research #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2404.06379

Abstract

Previous work has shown that the disarray (or displacement) of an (affine) (signed) permutation is bounded in terms of its Coxeter length. Here, we characterize the permutations for which the bound is sharp in two ways: in terms of a natural property of their reduced words, and by ``globally'' avoiding the pattern 321.

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