The intersection cohomology of Schubert varieties is a combinatorial invariant

We give an explicit and entirely poset-theoretic way to compute, for any permutation v, all the Kazhdan–Lusztig polynomials Px,y for x,y≤v, starting from the Bruhat interval [e,v] as an abstract poset. This proves, in particular, that the intersection cohomology of Schubert varieties depends only on the inclusion relations between the closures of its Schubert cells.