Construction of arbitrary Kazhdan-Lusztig polynomials

To each polynomial P with integral non-negative coefficients and constant t erm equal to 1, of degree d, we associate a pair of elements (y; w) in the symmetric group S-n, whets n = 1 + d + P(1), for which we pi-eve that the K azhdan-Lusztig polynomial P-y,P-w eqllals P. This pair satisfies l(w) - l(y ) = 2d + P(1) - 1, where l(w) denotes the number of inversions of w. (C) Ac ademie des Sciences/Elsevier, Paris.