Involution systems generalize Coxeter systems such that their weak orders are complete meet-semilattices for a broader class including cactus groups, with finite presentations for those with sign characters and new characterizations of Coxeter systems.
Garside shadows and biautomatic structures in Coxeter groups
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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math.GR 2verdicts
UNVERDICTED 2representative citing papers
Proves that inversion-set intersection sets in Coxeter groups are convex in weak order with unique minimal elements, enabling computational cone-type checks.
citing papers explorer
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Weak order on groups generated by involutions
Involution systems generalize Coxeter systems such that their weak orders are complete meet-semilattices for a broader class including cactus groups, with finite presentations for those with sign characters and new characterizations of Coxeter systems.
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Combinatorics of cone types in Coxeter groups
Proves that inversion-set intersection sets in Coxeter groups are convex in weak order with unique minimal elements, enabling computational cone-type checks.