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Algorithm demonstrates a new method to compute joins in the weak order of type B Coxeter groups, confirming prior conjectures.
We present an algorithm for computing the join of two elements in the weak order of the Coxeter group of type B. This extends Markowsky's algorithm for computing joins of standard permutations to signed permutations, and allows us to confirm a conjecture of Dyer concerning a geometric interpretation of these joins.
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Biagioli et al. (2026) studied this question.
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