Combinatorial Expansions of Kazhdan-Lusztig Polynomials |
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Authors: | Brenti Francesco |
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Affiliation: | School of Mathematics, Institute for Advanced Study Princeton, New Jersey 08540, USA |
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Abstract: | We introduce two related families of polynomials, easily computableby simple recursions into which any KazhdanLusztig (andinverse KazhdanLusztig) polynomial of any Coxeter groupcan be expanded linearly, and we give combinatorial interpretationsto the coefficients in these expansions. This yields a combinatorialrule for computing the KazhdanLusztig polynomials interms of paths in a directed graph, and a completely combinatorialreformulation of the nonnegativity conjecture [15, p. 166]. |
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