Equivariant Perturbation in Gomory and Johnson’s Infinite Group Problem. III. Foundations for the k-Dimensional Case with Applications to k=2

We develop foundational tools for classifying the extreme valid functions for the k-dimensional infinite group problem. In particular, (1) we present the general regular solution to Cauchy’s additive functional equation on bounded convex domains. This provides a k-dimensional generalization of the so-called interval lemma, allowing us to deduce affine properties of the function from certain … Read more