Separation of integer points by a hyperplane under some weak notions of discrete convexity

TL;DR

This paper introduces weaker conditions related to discrete convexity that ensure the separation of two sets of integer points by a hyperplane, expanding the theoretical understanding of discrete convex sets.

Contribution

It provides new sufficient conditions for separating integer point sets with hyperplanes, relaxing previous convexity assumptions.

Findings

Established weaker convexity-based separation conditions

Extended theoretical framework for discrete convex sets

Potential applications in integer programming and combinatorial optimization

Abstract

We give some sufficient conditions of separation of two sets of integer points by a hyperplane. Our conditions are related to the notion of convexity of sets of integer points and are weaker than existing notions.