Cayley sums and Minkowski sums of lattice polytopes

Abstract

In this paper, we discuss the integer decomposition property for Cayley sums and Minkowski sums of lattice polytopes. In fact, we characterize when Cayley sums have the integer decomposition property in terms of Minkowski sums. Moreover, by using this characterization, we consider when Cayley sums and Minkowski sums of 2-convex-normal lattice polytopes have the integer decomposition property. Finally, we also discuss the level property for Minkowski sums and Cayley sums.

Unimodular covers of 3-dimensional parallelepipeds and Cayley sums

“…Oda ([12]) posed several questions regarding smoothness and the IDP property for lattice polytopes. Following [6,16], we say that a pair (P, Q) of lattice polytopes has the integer decomposition property, or that the pair (P, Q) is IDP, if…”