A Shapley-Folkman lemma for lattice polytopes

TL;DR

This paper explores a specialized version of the Shapley-Folkman lemma, demonstrating that in certain cases, the number of summands can be reduced by one, which has implications for lattice polytopes.

Contribution

It introduces a new variant of the Shapley-Folkman lemma applicable to lattice polytopes, reducing the number of summands needed in specific cases.

Findings

Reduction of summands from n to n-1 in certain lattice polytope cases

Extension of the Shapley-Folkman lemma to lattice polytopes

Potential implications for optimization and combinatorics

Abstract

Some occurrences of $n$ can be replaced by $n-1$ in a special case of the Shapley-Folkman lemma.