Projecting Lattice Polytopes Without Interior Lattice Points
نویسندگان
چکیده
منابع مشابه
Projecting Lattice Polytopes Without Interior Lattice Points
We show that up to unimodular equivalence there are only finitely many d-dimensional lattice polytopes without interior lattice points that do not admit a lattice projection onto a (d− 1)-dimensional lattice polytope without interior lattice points. This was conjectured by Treutlein. As an immediate corollary, we get a short proof of a recent result of Averkov, Wagner &Weismantel, namely the fi...
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A theorem of Howe states that every 3-dimensional lattice polytope P whose only lattice points are its vertices, is a Cayley polytope, i.e. P is the convex hull of two lattice polygons with distance one. We want to generalize this result by classifying 3-dimensional lattice polytopes without interior lattice points. The main result will be, that they are up to finite many exceptions either Cayl...
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We show that, for any lattice polytope P ⊂ R, the set int(P ) ∩ lZ (provided it is non-empty) contains a point whose coefficient of asymmetry with respect to P is at most 8d · (8l+7) 2d+1 . If, moreover, P is a simplex, then this bound can be improved to 9 · (8l+ 7) d+1 . This implies that the maximum volume of a lattice polytope P ⊂ R d containing exactly k ≥ 1 points of lZ in its interior, is...
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We show that, for any lattice polytope P ⊂ R, the set int(P ) ∩lZ (provided it is non-empty) contains a point whose coefficient ofasymmetry with respect to P is at most 8d · (8l+7)2d+1. If, moreover,P is a simplex, then this bound can be improved to 8 · (8l+ 7)d+1.As an application, we deduce new upper bounds on the volume ofa lattice polytope, given its ...
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Lattice polytopes arise naturally in algebraic geometry, analysis, combinatorics, computer science, number theory, optimization, probability and representation theory. They possess a rich structure arising from the interaction of algebraic, convex, analytic, and combinatorial properties. In this chapter, we concentrate on the theory of lattice polytopes and only sketch their numerous applicatio...
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ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 2011
ISSN: 0364-765X,1526-5471
DOI: 10.1287/moor.1110.0503