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A breakthrough in the theory of (type A) Macdonald polynomials is due toHaglund, Haiman and Loehr, who exhibited a combinatorial formula for thesepolynomials in terms of fillings of Young diagrams. Recently, Ram and Yip gavea formula for the Macdonald polynomials of arbitrary type in terms of thecorresponding affine Weyl group. In this paper, we show that aHaglund-Haiman-Loehr type formula follows naturally from the more generalRam-Yip formula, via compression. Then we extend this approach to theHall-Littlewood polynomials of type C, which are specializations of thecorresponding Macdonald polynomials at q=0. We note that no analog of theHaglund-Haiman-Loehr formula exists beyond type A, so our work is a first steptowards finding such a formula.

Combinatorial Formulas for Macdonald and Hall-Littlewood Polynomials of Types A and C. Extended Abstract