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A Construction for Partitions Which Avoid Long Arithmetic Progressions

Published online by Cambridge University Press:  20 November 2018

E.R. Berlekamp
E.R. Berlekamp*
Affiliation:
Bell Telephone Laboratories Incorporated, Murray Hill, New Jersey
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For k ≥2, t ≥2, let W(k, t) denote the least integer m such that in every partition of m consecutive integers into k sets, atleast one set contains an arithmetic progression of t+1 terms. This paper presents a construction which improves the best previously known lower bounds on W(k, t) for small k and large t.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 3 , August 1968 , pp. 409 - 414
Copyright
Copyright © Canadian Mathematical Society 1968

References

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