In mathematics, the Grace–Walsh–Szegő coincidence theorem is a result named after John Hilton Grace, Joseph L. Walsh, and Gábor Szegő.
Statement
Suppose ƒ(z1, ..., zn) is a polynomial with complex coefficients, and that it is symmetric, i.e. invariant under permutations of the variables, and multi-affine, i.e. affine in each variable separately. Let A be a circular region in the complex plane. If either A is convex or the degree of ƒ is n, then for every there exists such that
Notes and references