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Remmel and Whitney provided an algorithmic procedure for determining the Littlewood-Richardson coefficients that appear in the Schur function expansion of a product of Schur functions. Haglund et al. introduced the quasisymmetric Schur functions as a basis for QSym. This paper adapts Remmel and Whitney's approach in order to determine the coefficients that appear in the quasisymmetric Schur function expansion of the product of a quasisymmetric Schur function and a (symmetric) Schur function.fatcat:lg4wnjqe35hwvjo5zjb4quh4hi