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Distance between vertices of lattice polytopes

Abstract : A lattice (d, k)-polytope is the convex hull of a set of points in dimension d whose coordinates are integers ranging between 0 and k. We consider the largest possible distance δ (d, k) between two vertices in the edge-graph of a lattice (d, k)-polytope. We show that δ (5, 3) and δ (3, 6) are equal to 10. This substantiates the conjecture whereby δ (d, k) is achieved by a Minkowski sum of lattice vectors.
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Contributor : Antoine Deza Connect in order to contact the contributor
Submitted on : Tuesday, November 2, 2021 - 10:59:33 PM
Last modification on : Saturday, November 6, 2021 - 4:22:20 AM


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Anna Deza, Antoine Deza, Zhongyan Guan, Lionel Pournin. Distance between vertices of lattice polytopes. Optimization Letters, Springer Verlag, 2020, 14 (2), pp.309-326. ⟨10.1007/s11590-018-1338-7⟩. ⟨hal-03412184⟩



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