Abstract
Let (W, S) be an arbitrary Coxeter system, y ∊ S*. We describe an algorithm which will compute, directly from y and the Coxeter matrix of W, the interval from the identity to y in the Bruhat ordering, together with the (partially defined) left and right actions of the generators. This provides us with exactly the data that are needed to compute the Kazhdan-Lusztig polynomials P x, z , x ≤ z ≤ y. The correctness proof of the algorithm is based on a remarkable theorem due to Matthew Dyer
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