Geodesic
Lattice points in Minkowski sums
The electronic journal of combinatorics, Tome 15 (2008)

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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 $P$.
DOI : 10.37236/886
Classification : 52B20, 14M25 
Christian Haase; Benjamin Nill; Andreas Paffenholz; Francisco Santos. Lattice points in Minkowski sums. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/886
@article{10_37236_886,
     author = {Christian Haase and Benjamin Nill and Andreas Paffenholz and Francisco Santos},
     title = {Lattice points in {Minkowski} sums},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/886},
     zbl = {1160.52009},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/886/}
}
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