Perriello, Andrew
(2011)
Lattice-Free Simplexes in Dimension 4.
Master's Thesis, University of Pittsburgh.
(Unpublished)
Abstract
We use a numerical approach to discover lattice free simplexes in dimension 4 with width at least 3. We follow the methodologies of Mori, Morrison, and Morrison and use a theoretical result proven by Barille, Bernardi, Borisov, and Kantor to conjecture a complete list of empty-lattice simplexes in dimension 4. Similar work was done by Haase and Ziegler, however, using a different approach we were able to both produce more evidence for the conjecture and provide an explicit list of distinct empty-lattice simplexes in dimension 4.
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Details
| Item Type: |
University of Pittsburgh ETD
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| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
27 January 2011 |
| Date Type: |
Completion |
| Defense Date: |
6 December 2010 |
| Approval Date: |
27 January 2011 |
| Submission Date: |
8 December 2010 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
MS - Master of Science |
| Thesis Type: |
Master's Thesis |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
empty-lattice simplex cones polytopes classificati |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-12082010-143132/, etd-12082010-143132 |
| Date Deposited: |
10 Nov 2011 20:09 |
| Last Modified: |
15 Nov 2016 13:53 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/10216 |
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