2021/11/14 by Moriguchi, Satoko, Murota, Kazuo
#52A41 #90C25 #90C27 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2111.07240
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-natural-convexity is a special case of integral convexity, and the combination of L-natural-convexity and M-natural-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-natural-convexity and M-natural-convexity.