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Distance between vertices of lattice polytopes
Journal article

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$$\delta $$(d,k) between two vertices in the edge-graph of a lattice (d,k)-polytope. We show that δ$$\delta $$(5,3) and δ$$\delta $$(3,6) are equal to 10. This substantiates the conjecture whereby δ$$\delta $$(d,k) is achieved by a Minkowski sum of lattice vectors.

Authors

Deza A; Deza A; Guan Z; Pournin L

Journal

Optimization Letters, Vol. 14, No. 2, pp. 309–326

Publisher

Springer Nature

Publication Date

March 1, 2020

DOI

10.1007/s11590-018-1338-7

ISSN

1862-4472

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