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Generalizing the Algebra of Throws to Rank-3 Matroids

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posted on 15.11.2021, 17:23 by Jasmine HallJasmine Hall

The algebra of throws is a geometric construction which reveals the underlying algebraic operations of addition and multiplication in a projective plane. In Desarguesian projective planes, the algebra of throws is a well-defined, commutative and associative binary operation. However, when we consider an analogous operation in a more general point-line configuration that comes from rank-3 matroids, none of these properties are guaranteed. We construct lists of forbidden configurations which give polynomial time checks for certain properties. Using these forbidden configurations, we can check whether a configuration has a group structure under this analogous operation. We look at the properties of configurations with such a group structure, and discuss their connection to the jointless Dowling geometries.

History

Copyright Date

01/01/2016

Date of Award

01/01/2016

Publisher

Te Herenga Waka—Victoria University of Wellington

Rights License

Author Retains Copyright

Degree Discipline

Mathematics

Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level

Masters

Degree Name

Master of Science

ANZSRC Type Of Activity code

1 PURE BASIC RESEARCH

Victoria University of Wellington Item Type

Awarded Research Masters Thesis

Language

en_NZ

Victoria University of Wellington School

School of Mathematics, Statistics and Operations Research

Advisors

Whittle, Geoff