INCLUSION AND INTERSECTION RELATIONS BETWEEN FUNDAMENTAL CLASSES OF DISCRETE CONVEX FUNCTIONS

Abstract

In discrete convex analysis, various convexity concepts are considered for discrete functions such as separable convexity, L-convexity, M-convexity, integral convexity, and multimodularity. These concepts of discrete convex functions are not mutually independent. For example, M^♮-convexity is a special case of integral convexity, and the combination of L^♮-convexity and M^♮-convexity coincides with separable convexity. This paper aims at a fairly comprehensive analysis of the inclusion and intersection relations for various classes of discrete convex functions. Emphasis is put on the analysis of multimodularity in relation to L^♮-convexity and M^♮-convexity.