## Equivariant Perturbation in Gomory and Johnson’s Infinite Group Problem. VII. Inverse semigroup theory, closures, decomposition of perturbations

In this self-contained paper, we present a theory of the piecewise linear minimal valid functions for the 1-row Gomory-Johnson infinite group problem. The non-extreme minimal valid functions are those that admit effective perturbations. We give a precise description of the space of these perturbations as a direct sum of certain finite- and infinite-dimensional subspaces. The … Read more