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Interpolation by symmetric functions and alternating higher Bruhat orders

We study interpolation by Grassmannian Schubert polynomials (Schur functions). We prove versions of the Sturmfels-Zelevinsky formula for the product of the maximal minors of rectangular matrices corresponding to elementary symmetric functions and Schur functions, and deduce from them generalizations of formulae for the Cauchy-Vandermonde determinant and Cauchy's formula for Schur functions. We define generalizations of higher Bruhat orders whose elements encode connected components of configuration spaces, and also generalizations of discriminantal Manin-Schechtman arrangements.