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 families in Artin-Tits monoids and low elements in Coxeter groups.Comptes Rendus Mathematique, 353:403–408
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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.