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A Lattice Point Problem Related to Sets Containing No l-Term Arithmetic Progression

Published online by Cambridge University Press:  20 November 2018

J. Riddell
J. Riddell*
Affiliation:
University of Victoria, Victoria, British Columbia
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In 1927 van der Waerden [6] proved that given positive integers k and l, there exists an integer W such that if 1, 2, …, W are partitioned into k or fewer classes, then at least one class contains an l-term arithmetic progression (l-progression). Let W(k, l), be the smallest such integer W. It would be of interest to find a reasonable upper estimate for W(k, l), say one that could be written down.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 4 , December 1971 , pp. 535 - 538
Copyright
Copyright © Canadian Mathematical Society 1971

References

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