Geodesic
Rationally smooth elements of Coxeter groups and triangle group avoidance.
Journal of Algebraic Combinatorics, Tome 39 (2014) no. 3, pp. 659-681.

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

We study a family of infinite-type Coxeter groups defined by the avoidance of certain rank 3 parabolic subgroups. For this family, rationally smooth elements can be detected by looking at only a few coefficients of the Poincaré polynomial. We also prove a factorization theorem for the Poincaré polynomial of rationally smooth elements. As an application, we show that a large class of infinite-type Coxeter groups have only finitely many rationally smooth elements. Explicit enumerations and descriptions of these elements are given in special cases.
Classification : 20F55, 20F05, 05E15, 14M15
Keywords: Coxeter groups, Poincaré polynomials, palindromic polynomials, palindromic elements, Schubert varieties, rational smoothness, triangle groups, pattern avoidance 
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     author = {Richmond, Edward and Slofstra, William},
     title = {Rationally smooth elements of {Coxeter} groups and triangle group avoidance.},
     journal = {Journal of Algebraic Combinatorics},
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Richmond, Edward; Slofstra, William. Rationally smooth elements of Coxeter groups and triangle group avoidance.. Journal of Algebraic Combinatorics, Tome 39 (2014) no. 3, pp. 659-681. http://geodesic.mathdoc.fr/item/JAC_2014__39_3_a5/