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|Title:||Computational determination of the largest lattice polytope diameter|
|Department:||Computing and Software|
|Abstract:||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.|
|Appears in Collections:||Open Access Dissertations and Theses|
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|Chadder_Nathan_S_2017Sept_MASc.pdf||370.59 kB||Adobe PDF||View/Open|
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