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.