Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/22226
Title: | Computational determination of the largest lattice polytope diameter |
Authors: | Chadder, Nathan |
Advisor: | Deza, Antoine |
Department: | Computing and Software |
Publication Date: | 2017 |
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. |
URI: | http://hdl.handle.net/11375/22226 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Chadder_Nathan_S_2017Sept_MASc.pdf | 370.59 kB | Adobe PDF | View/Open |
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