Lattice points in Minkowski sums
Combinatorics
2020-01-14 v1 Commutative Algebra
Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.0711.4393,
title = {Lattice points in Minkowski sums},
author = {Christian Haase and Benjamin Nill and Andreas Paffenholz and Francisco Santos},
journal= {arXiv preprint arXiv:0711.4393},
year = {2020}
}
Comments
5 pages, 4 figures