Unique Minimal Liftings for Simplicial Polytopes

Details Unique Minimal Liftings for Simplicial Polytopes Unique Minimal Liftings for Simplicial Polytopes

2011-03-21

arxiv.org/abs/1103.4112v2

Mathematics

Optimization and Control

15 pages

Scientific paper

For a minimal inequality derived from a maximal lattice-free simplicial polytope in $\R^n$, we investigate the region where minimal liftings are uniquely defined, and we characterize when this region covers $\R^n$. We then use this characterization to show that a minimal inequality derived from a maximal lattice-free simplex in $\R^n$ with exactly one lattice point in the relative interior of each facet has a unique minimal lifting if and only if all the vertices of the simplex are lattice points.

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