Geodesic
On 321-avoiding permutations in affine Weyl groups
Journal of Algebraic Combinatorics, Tome 15 (2002) no. 3, pp. 241-252.

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

Summary: We introduce the notion of 321-avoiding permutations in the affine Weyl group $W$ of type $A _{ n - 1}$ by considering the group as a George group (in the sense of Eriksson and Eriksson). This enables us to generalize a result of Billey, Jockusch and Stanley to show that the 321-avoiding permutations in $W$ coincide with the set of fully commutative elements; in other words, any two reduced expressions for a 321-avoiding element of $W$ (considered as a Coxeter group) may be obtained from each other by repeated applications of short braid relations. Using Shi's characterization of the Kazhdan-Lusztig cells in the group $W$, we use our main result to show that the fully commutative elements of $W$ form a union of Kazhdan-Lusztig cells. This phenomenon has been studied by the author and J. Losonczy for finite Coxeter groups, and is interesting partly because it allows certain structure constants for the Kazhdan-Lusztig basis of the associated Hecke algebra to be computed combinatorially.
Keywords: pattern avoidance, Kazhdan-Lusztig cells 
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     author = {Green, R.M.},
     title = {On 321-avoiding permutations in affine {Weyl} groups},
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Green, R.M. On 321-avoiding permutations in affine Weyl groups. Journal of Algebraic Combinatorics, Tome 15 (2002) no. 3, pp. 241-252. http://geodesic.mathdoc.fr/item/JAC_2002__15_3_a3/