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A combinatorial formula for Macdonald polynomials

Authors:	J Haglund M Haiman N Loehr

Institution:	Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395 ; Department of Mathematics, University of California, Berkeley, California 97420-3840 N. Loehr ; Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395

Abstract:	We prove a combinatorial formula for the Macdonald polynomial $\tilde{H}_{\mu }(x;q,t)$ which had been conjectured by Haglund. Corollaries to our main theorem include the expansion of $\tilde{H}_{\mu }(x;q,t)$ in terms of LLT polynomials, a new proof of the charge formula of Lascoux and Schützenberger for Hall-Littlewood polynomials, a new proof of Knop and Sahi's combinatorial formula for Jack polynomials as well as a lifting of their formula to integral form Macdonald polynomials, and a new combinatorial rule for the Kostka-Macdonald coefficients $\tilde{K}_{\lambda \mu }(q,t)$ in the case that $\mu$ is a partition with parts $\leq 2$ .

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