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Intersection Theorems for Systems of Sets

Published online by Cambridge University Press:  20 November 2018

Joel Spencer
Joel Spencer*
Affiliation:
Dept. of Math., State University of New York at Stony Brook, Stony BrookNew York 11794 U.S.A.
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Let n and k be positive integers, k≥3. Denote by ϕ(n, k) the least positive integer such that if F is any family of more than ϕ(n, k) sets, each set with n elements, then some k members of F have pairwise the same intersection. In this paper we obtain a new asymptotic upper bound for ϕ(n, k), k fixed, n approaching infinity.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 2 , 01 June 1977 , pp. 249 - 254
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Abbott, H. L., Hanson, D., and Sauer, N., Intersection theorems for systems of sets, J. Combinatorial Theory 12 (1972), 381-389.Google Scholar
2. Erdös, P. and Rado, R., Intersection theorems for systems of sets, J. London Math. Soc. 35 (1960), 85-90.Google Scholar