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Variations on a theorem by van der Waerden

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.

  1. http://hdl.handle.net/1993/321
Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:MWU.1993/321
Date10 April 2007
CreatorsJohannson, Karen R
ContributorsGunderson, David (Mathematics), Craigen, Robert (Mathematics) Padmanabhan, Ranganathan (Mathematics) Landman, Bruce (State University of West Georgia)
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
Languageen_US
Detected LanguageEnglish

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