  Macdonald polynomials are orthogonal polynomials associated to root systems,
and in the type A case, the symmetric kind is a common generalization of Schur
functions, Macdonald spherical functions, and Jack polynomials. We use the
combinatorics of alcove walks to calculate products of monomials and
intertwining operators of the double affine Hecke algebra. From this, we obtain
a product formula for Macdonald polynomials of general type.
