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Mcdonald polynomials are symmetric polynomials with coefficients in the field of fractions k(q,t). Algebraically they are of much interest because some of their specializations are other studied polynomials, for example setting q=0 gives Hall-Littlewood polynomials, and q=t gives the classical Schur functions. Combinatorially some of their properties can be thought as q-analogs of classical identities. And there is also a geometric side: being symmetric they can be expanded in terms of Schur functions with coefficients in k(q,t). Mcdonald conjectured that the coefficients were actual polynomials (not just rational functions) with nonnegative coefficients. The conjecture was settled by Mark Haiman using the geometry of Hilbert Schemes of points in the plane.