# Convexity of distinct sum sets

## TL;DR

This paper investigates whether sum sets derived from lattice points of convex polytopes also form convex lattice polytopes, providing positive results in two dimensions and negative in higher dimensions, with applications to corner cut polyhedra.

## Contribution

It establishes dimension-dependent results on the convexity of sum sets from lattice points and applies findings to the study of corner cut polyhedra.

## Key findings

- Positive in 2D for convex lattice polytopes
- Negative in higher dimensions
- Application to corner cut polyhedron

## Abstract

We study a combinatorial notion where given a set of lattice points one takes the set of all sums of subsets of a fixed size, and we ask if the given set comes from a convex lattice polytope whether the resulting set also comes from a convex lattice polytope. We obtain a positive result in dimension 2 and a negative result in higher dimensions. We apply this to the corner cut polyhedron.