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Journal of the London Mathematical Society 1997 55(3):448-472; doi:10.1112/S0024610797004948
© 1997 by London Mathematical Society
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© The London Mathematical Society

Combinatorial Expansions of Kazhdan–Lusztig Polynomials

Francesco Brenti

School of Mathematics, Institute for Advanced Study Princeton, New Jersey 08540, USA

Received 9 January 1995.

We introduce two related families of polynomials, easily computable by simple recursions into which any Kazhdan–Lusztig (and inverse Kazhdan–Lusztig) polynomial of any Coxeter group can be expanded linearly, and we give combinatorial interpretations to the coefficients in these expansions. This yields a combinatorial rule for computing the Kazhdan–Lusztig polynomials in terms of paths in a directed graph, and a completely combinatorial reformulation of the nonnegativity conjecture [15, p. 166].


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