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Using the combinatorial formula for the transformed Macdonald polynomials of Haglund, Haiman, and Loehr, we investigate the combinatorics of the symmetry relation H µ (x; q, t) = H µ * (x; t, q). We provide a purely combinatorial proof of the relation in the case of Hall-Littlewood polynomials (q = 0) when µ is a partition with at most three rows, and for… (More)

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