English

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

Combinatorics 2024-04-10 v1

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.

Keywords

Cite

@article{arxiv.2404.06379,
  title  = {Disarray, reduced words, and 321-avoidance in George groups},
  author = {Joel Brewster Lewis and Bridget Eileen Tenner},
  journal= {arXiv preprint arXiv:2404.06379},
  year   = {2024}
}

Comments

16 pages; comments welcome!

R2 v1 2026-06-28T15:48:55.114Z