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.
Davis.The geometry and topology of Coxeter groups, volume 32 ofLondon Mathematical Society Monographs Series
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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.