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Article Dans Une Revue Discrete Applied Mathematics Année : 2020

Computational determination of the largest lattice polytope diameter

Résumé

A lattice (d, k)-polytope is the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. Let δ(d, k) be the largest diameter over all lattice (d, k)-polytopes. We develop a computational framework to determine δ(d, k) for small instances. We show that δ(3, 4) = 7 and δ(3, 5) = 9; that is, we verify for (d, k) = (3, 4) and (3, 5) the conjecture whereby δ(d, k) is at most (k + 1)d/2 and is achieved, up to translation, by a Minkowski sum of lattice vectors.
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hal-03409935 , version 1 (30-10-2021)

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Nathan Chadder, Antoine Deza. Computational determination of the largest lattice polytope diameter. Discrete Applied Mathematics, 2020, 281, pp.106-110. ⟨10.1016/j.dam.2019.10.026⟩. ⟨hal-03409935⟩
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