Lattice points in Minkowski sums

Christian Haase, Benjamin Nill, Andreas Paffenholz, Francisco Santos

Published 2007-11-28Version 1

Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact that does not need the smoothness assumption on P.