English

Shapley-Folkman-type Theorem for Integrally Convex Sets

Combinatorics 2024-08-20 v2

Abstract

The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex sets, L-natural-convex sets, and M-natural-convex sets, which are major classes of discrete convex sets in discrete convex analysis.

Keywords

Cite

@article{arxiv.2305.15125,
  title  = {Shapley-Folkman-type Theorem for Integrally Convex Sets},
  author = {Kazuo Murota and Akihisa Tamura},
  journal= {arXiv preprint arXiv:2305.15125},
  year   = {2024}
}

Comments

13 pages

R2 v1 2026-06-28T10:44:33.850Z