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Title: Variations on a theorem by van der Waerden
Authors: Johannson, Karen R
Supervisor: Gunderson, David (Mathematics)
Examining Committee: Craigen, Robert (Mathematics) Padmanabhan, Ranganathan (Mathematics) Landman, Bruce (State University of West Georgia)
Graduation Date: May 2007
Keywords: combinatorics
arithmetic progressions
Issue Date: 10-Apr-2007
Abstract: The central result presented in this thesis is van der Waerden's theorem on arithmetic progressions. Van der Waerden's theorem guarantees that for any integers k and r, there is an n so that however the set {1, 2, ... , n} is split into r disjoint partition classes, at least one partition class will contain a k-term arithmetic progression. Presented here are a number of variations and generalizations of van der Waerden's theorem that utilize a wide range of techniques from areas of mathematics including combinatorics, number theory, algebra, and topology.
Appears in Collection(s):FGS - Electronic Theses & Dissertations (Public)

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