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On sets of integers not containing arithmetic progressions of prescribed length

Published online by Cambridge University Press:  09 April 2009

H. L. Abbott ,
A. C. Liu  and
J. Riddell
H. L. Abbott
Affiliation:
University of Alberta, Edmonton, Alberta
A. C. Liu
Affiliation:
University of Alberta, Edmonton, Alberta
J. Riddell
Affiliation:
University of Victoria, Victoria, British Columbia
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Let m, n and l be positive integers satisfying m ≦ n ≦ l ≦ 3. Denote by h(m, n, l) the largest integer with the property that from every n-subset of {1,2, …, m} one can select h(m, n, l) integers no l of which are in arithmetic progression. Let f(n, l) = h(n, n, l) and let g(n, l) = minmh(m, n, l). In what follows, by a P1-free set we shall mean a set of integers not containing an arithmetic progression of length l.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 2 , September 1974 , pp. 188 - 193
Copyright
Copyright © Australian Mathematical Society 1974

References

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