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arXiv · 2609.25395

On inversion sets of joins in weak Bruhat order

Ming Yean Lim
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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.

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Ming Yean Lim. 2026-09-21. On inversion sets of joins in weak Bruhat order. https://arxiv.org/abs/2609.25395

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