English

Bruhat order and graph structures of lower intervals in Coxeter groups

Combinatorics 2018-12-18 v1

Abstract

We show that any lower Bruhat interval in a Coxeter group is a disjoint union of certain two-sided cosets as a consequence of Lifting Property and Subword Property. Furthermore, we describe these details in terms of Bruhat graphs, graded posets, and two-sided quotients altogether. For this purpose, we introduce some new ideas, quotient lower intervals and quotient Bruhat graphs.

Keywords

Cite

@article{arxiv.1812.06266,
  title  = {Bruhat order and graph structures of lower intervals in Coxeter groups},
  author = {Masato Kobayashi},
  journal= {arXiv preprint arXiv:1812.06266},
  year   = {2018}
}

Comments

18 pages

R2 v1 2026-06-23T06:43:22.617Z