Year: 2026
Type: preprint
Abstract: It is well-known that any Coxeter group $W$ is a meet-semilattice with respect to weak order. Furthermore, when $W$ is finite, it is a lattice. In the first part of this paper, we give a recursive algorithm that computes joins in weak order for arbitrary finite $W$. In the second part, we complete the proof of a conjecture of Dyer expressing the inversion set of a join in terms of the union of inversion sets of each factor, under the assumption that $W$ is finite. Some proofs were developed in collaboration with Claude Opus 5.
Source: arXiv (Cornell University)
Author: Lim, Ming Yean
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7214092073