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, \(\hbox {L}^{\natural }\)-convex sets, and \(\hbox {M}^{\natural }\)-convex sets.