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{\bf Christian Haase, Benjamin Nill, Andreas Paffenholz and Francisco Santos}
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{\bf Lattice Points in Minkowski Sums}
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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 $P$.

\bye

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