Geodesic
On the fully commutative elements of Coxeter groups
Journal of Algebraic Combinatorics, Tome 5 (1996) no. 4, pp. 353-385.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $W$ be a Coxeter group. We define an element $w \epsilon W$ to be fully commutative if any reduced expression for $w$ can be obtained from any other by means of braid relations that only involve $commuting$ generators. We give several combinatorial characterizations of this property, classify the Coxeter groups with finitely many fully commutative elements, and classify the parabolic quotients whose members are all fully commutative. As applications of the latter, we classify all parabolic quotients with the property that (1) the Bruhat ordering is a lattice, (2) the Bruhat ordering is a distributive lattice, (3) the weak ordering is a distributive lattice, and (4) the weak ordering and Bruhat ordering coincide.
Keywords: Coxeter group, reduced word, heap, weak order, Bruhat order 
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     author = {Stembridge, John R.},
     title = {On the fully commutative elements of {Coxeter} groups},
     journal = {Journal of Algebraic Combinatorics},
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Stembridge, John R. On the fully commutative elements of Coxeter groups. Journal of Algebraic Combinatorics, Tome 5 (1996) no. 4, pp. 353-385. http://geodesic.mathdoc.fr/item/JAC_1996__5_4_a0/