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Lattice-Free Simplexes in Dimension 4

Perriello, Andrew (2011) Lattice-Free Simplexes in Dimension 4. Master's Thesis, University of Pittsburgh. (Unpublished)

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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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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Perriello, Andrewacp27@pitt.eduACP27
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairBorisov, Alexanderborisov@pitt.eduBORISOV
Committee MemberIon, Bogdanbion@pitt.eduBION
Committee MemberKaveh, Kiumarskaveh@pitt.eduKAVEH
Committee MemberGartside, Paulgartside@math.pitt.eduPMG20
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:, etd-12082010-143132
Date Deposited: 10 Nov 2011 20:09
Last Modified: 15 Nov 2016 13:53


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