Computational determination of the largest lattice polytope diameter
| dc.contributor.advisor | Deza, Antoine | |
| dc.contributor.author | Chadder, Nathan | |
| dc.contributor.department | Computing and Software | en_US |
| dc.date.accessioned | 2017-10-17T12:43:44Z | |
| dc.date.available | 2017-10-17T12:43:44Z | |
| dc.date.issued | 2017 | |
| dc.description.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. | en_US |
| dc.description.degree | Master of Applied Science (MASc) | en_US |
| dc.description.degreetype | Thesis | en_US |
| dc.identifier.uri | http://hdl.handle.net/11375/22226 | |
| dc.language.iso | en | en_US |
| dc.title | Computational determination of the largest lattice polytope diameter | en_US |
| dc.type | Thesis | en_US |