Geodesic
The enumeration of fully commutative elements of Coxeter groups
Journal of Algebraic Combinatorics, Tome 7 (1998) no. 3, pp. 291-320.

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Summary: A Coxeter group element w is fully commutative if any reduced expression for w can be obtained from any other via the interchange of commuting generators. For example, in the symmetric group of degree n, the number of fully commutative elements is the nth Catalan number. The Coxeter groups with finitely many fully commutative elements can be arranged into seven infinite families A $_{n}$, B $_{n}$, D $_{n}$, E $_{n}$,F $_{n}$, H $_{n}$ and I $_{2}(m)$. For each family, we provide explicit generating functions for the number of fully commutative elements and the number of fully commutative involutions; in each case, the generating function is algebraic.
Keywords: Coxeter group, reduced word, braid relation 
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     author = {Stembridge, John R.},
     title = {The enumeration of fully commutative elements of {Coxeter} groups},
     journal = {Journal of Algebraic Combinatorics},
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Stembridge, John R. The enumeration of fully commutative elements of Coxeter groups. Journal of Algebraic Combinatorics, Tome 7 (1998) no. 3, pp. 291-320. http://geodesic.mathdoc.fr/item/JAC_1998__7_3_a1/