Geodesic
Leading coefficients of Kazhdan-Lusztig polynomials for Deodhar elements.
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 2, pp. 229-260.

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

Summary: We show that the leading coefficient of the Kazhdan-Lusztig polynomial $P _{ x, w }( q)$ known as $\mu ( x, w)$ is always either 0 or 1 when $w$ is a Deodhar element of a finite Weyl group. The Deodhar elements have previously been characterized using pattern avoidance in Billey and Warrington (J. Algebraic Combin. $13(2)$:111-136, [ 2001]) and Billey and Jones (Ann. Comb. [ 2008], to appear). In type $A$, these elements are precisely the 321-hexagon avoiding permutations. Using Deodhar's algorithm (Deodhar in Geom. Dedicata $63(1)$:95-119, [ 1990]), we provide some combinatorial criteria to determine when $\mu ( x, w)=1$ for such permutations $w$.
Keywords: keywords Kazhdan-Lusztig polynomial, 321-hexagon, 0-1 conjecture, pattern avoidance 
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     title = {Leading coefficients of {Kazhdan-Lusztig} polynomials for {Deodhar} elements.},
     journal = {Journal of Algebraic Combinatorics},
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Jones, Brant C. Leading coefficients of Kazhdan-Lusztig polynomials for Deodhar elements.. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 2, pp. 229-260. http://geodesic.mathdoc.fr/item/JAC_2009__29_2_a1/