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Sums of Sets of Lattice Points and Unimodular Coverings of Polytopes by Nathanson, Melvyn B. is a scholarly article available to read on EtoBox.

What is Sums of Sets of Lattice Points and Unimodular Coverings of Polytopes about?

If $P$ is a lattice polytope (that is, the convex hull of a finite set of lattice points in $\mathbf{R}^n$), then every sum of $h$ lattice points in $P$ is a lattice point in the $h$-fold sumset $hP$. However, a lattice point in the $h$-fold sumset $hP$ is not necessarily the sum of $h$ lattice points in $P$. It is proved that if the polytope $P$ is a union of unimodular simplices, then every lattice point in the $h$-fold sumset $hP$ is the sum of $h$ lattice points in $P$.

Author

Nathanson, Melvyn B.

Published

2015

Language

EN