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dc.contributor.supervisor Gunderson, David (Mathematics) en_US
dc.contributor.author Desmarais, Colin
dc.date.accessioned 2017-09-05T14:25:38Z
dc.date.available 2017-09-05T14:25:38Z
dc.date.issued 2017
dc.identifier.uri http://hdl.handle.net/1993/32418
dc.description.abstract An equation or system of equations is called ``partition regular in a set S" if and only if for any finite colouring of S a solution to the system is guaranteed to be contained in some colour class. This thesis is a survey of partition regular systems, starting with early results in arithmetic Ramsey theory, including Hilbert's cube lemma, Schur's theorem, and van der Waerden's theorem. A proof is given of Rado's characterization of all finite partition regular systems of homogeneous linear equations, and results concerning infinite and nonlinear partition regular systems are also proved. Several tools, including linear algebra and topology, are used in the proofs in this thesis. en_US
dc.subject combinatorics en_US
dc.subject arithmetic Ramsey theory en_US
dc.title On partition regular systems en_US
dc.degree.discipline Mathematics en_US
dc.contributor.examiningcommittee Craigen, Robert (Mathematics) Kocay, William (Computer Science) en_US
dc.degree.level Master of Science (M.Sc.) en_US
dc.description.note October 2017 en_US


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