Variations on a theorem by van der Waerden
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Date
2007-04-10T15:29:06Z
Authors
Johannson, Karen R
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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.
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Keywords
combinatorics, arithmetic progressions