Disarray, reduced words, and 321-avoidance in George groups
Joel Brewster Lewis, Bridget Eileen Tenner · arXiv (Cornell University) · 2024
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.