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Some Remarks on a Combinatorial Theorem of Erdös and Rado

Published online by Cambridge University Press:  20 November 2018

H. L. Abbott
H. L. Abbott*
Affiliation:
University of Alberta, Edmonton
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P. Erdös and R. Rado [1] proved that to each pair of positive integers n and k, with k ≥ 3, there corresponds a least positive integer φ(n, k) such that if is a family of more than φ(n, k) sets, each set with n elements, then some k of the sets have pair-wise the same intersection.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 2 , June 1966 , pp. 155 - 160
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Erdös, P. and Rado, R., Intersection theorems for systems of sets, Jour. Lon. Math. Soc, 35 (1960) pp. 85-90.Google Scholar
2. Erdös, P., On a problem in elementary number theory and a combinatorial problem. Math. of Comp., 18, No. 88, (1964) pp. 644-646.Google Scholar