A combinatorial formula for Macdonald polynomials
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 by J. Haglund, M. Haiman and N. Loehr PDF
 J. Amer. Math. Soc. 18 (2005), 735761 Request permission
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 SchĂĽtzenberger for HallLittlewood polynomials, a new proof of Knop and Sahiâ€™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 KostkaMacdonald coefficients $\tilde {K}_{\lambda \mu }(q,t)$ in the case that $\mu$ is a partition with parts $\leq 2$.References

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Additional Information
 J. Haglund
 Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 191046395
 MR Author ID: 600170
 Email: jhaglund@math.upenn.edu
 M. Haiman
 Affiliation: Department of Mathematics, University of California, Berkeley, California 974203840
 N. Loehr
 Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 191046395
 Address at time of publication: Department of Mathematics, College of William & Mary, Williamsburg, Virginia 231878795
 Email: nloehr@math.upenn.edu, nick@math.wm.edu
 Received by editor(s): October 18, 2004
 Published electronically: April 8, 2005
 Additional Notes: The first authorâ€™s work was supported by NSA grant MSPF02G193
The second authorâ€™s work was supported by NSF grant DMS0301072
The third authorâ€™s work was supported by an NSF Postdoctoral Research Fellowship  © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.  Journal: J. Amer. Math. Soc. 18 (2005), 735761
 MSC (2000): Primary 05E10; Secondary 05A30
 DOI: https://doi.org/10.1090/S0894034705004856
 MathSciNet review: 2138143