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ABSTRACT:
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 $\leq 2$.

SUGGESTED CITATION:
J Haglund, Mark Haiman, and N Loehr, "A combinatorial formula for Macdonald polynomials" (2005). Journal of the American Mathematical Society. 18 (3), pp. 735-761. Postprint available free at: http://repositories.cdlib.org/postprints/1135