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.
| Identifer | oai:union.ndltd.org:MANITOBA/oai:mspace.lib.umanitoba.ca:1993/321 |
| Date | 10 April 2007 |
| Creators | Johannson, Karen R |
| Contributors | Gunderson, David (Mathematics), Craigen, Robert (Mathematics) Padmanabhan, Ranganathan (Mathematics) Landman, Bruce (State University of West Georgia) |
| Source Sets | University of Manitoba Canada |
| Language | en_US |
| Detected Language | English |
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