English

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

R2 v1 2026-06-21T09:48:01.140Z