Geodesic
Polygon posets and the weak order of Coxeter groups
Journal of Algebraic Combinatorics, Tome 4 (1995) no. 3, pp. 233-252.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: We explore the connection between polygon posets, which is a class of ranked posets with an edge-labeling which satisfies certain lsquopolygon properties rsquo, and the weak order of Coxeter groups. We show that every polygon poset is isomorphic to a join ideal in the weak order, and for Coxeter groups where no pair of generators have infinite order the converse is also true. The class of polygon posets is seen to include the class of generalized quotients defined by Björner and Wachs, while itself being included in the class of alternative generalized quotients also considered by these authors. By studying polygon posets we are then able to answer an open question about common properties of these two classes.
Mots-clés : polygon poset, weak order, Coxeter group, generalized quotient, finite state automaton 
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     author = {Eriksson, Kimmo},
     title = {Polygon posets and the weak order of {Coxeter} groups},
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Eriksson, Kimmo. Polygon posets and the weak order of Coxeter groups. Journal of Algebraic Combinatorics, Tome 4 (1995) no. 3, pp. 233-252. https://geodesic-test.mathdoc.fr/item/JAC_1995__4_3_a1/