Decomposition of an Integrally Convex Set into a Minkowski Sum of Bounded and Conic Integrally Convex Sets

Abstract

Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar statements for some classes of discrete sets in discrete convex analysis, such as integrally convex sets, L-natural-convex sets, and M-natural-convex sets.