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dc.contributor.supervisor Padmanabhan, Ranganathan (Mathematics) en_US
dc.contributor.author Lanyon, Jeffrey
dc.date.accessioned 2018-03-29T20:41:05Z
dc.date.available 2018-03-29T20:41:05Z
dc.date.issued 2017
dc.date.submitted 2018-03-19T14:57:49Z en
dc.identifier.uri http://hdl.handle.net/1993/32915
dc.description.abstract One of the basic questions in this topic is about the "existence" and the related "realization" of abstract configurations. Motivated by the fact that a non-singular cubic curve in the projective plane over a field admits a geometrically defined group law "⊕" such that three points {P, Q, R} are collinear if and only if the sum P⊕Q⊕R = 0 under the group law, we define the concept of group realization of a given (nk) configuration. Group realizations are in turn used to construct geometric realizations (of (n3)'s and (n4)'s) in the real or the complex projective plane. Using a variety of techniques from algebra and number theory like the resultant of polynomials, Hensel's Lemma on lifting primitive roots to prime powers, companion matrices, and Bunyakovsky's conjecture we prove the existence of infinitely many realizable configurations, including: 1. Realizations of cyclic (n3) configurations using the group structure on cubic curves over the real or the complex plane; 2. Realizations of cyclic (n4) configurations using the group structure on non-circular ellipses where now blocks of 4 points are circles over the real plane. en_US
dc.subject Mathematics, Geometry, Configurations, Groups en_US
dc.title Group realizations of configurations en_US
dc.degree.discipline Mathematics en_US
dc.contributor.examiningcommittee Kirkland, Stephen (Mathematics) Zhang, Yang (Mathematics) Kocay, William (Computer Science) en_US
dc.degree.level Master of Science (M.Sc.) en_US
dc.description.note May 2018 en_US


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