Families of finite sets satisfying an intersection condition
- 1 August 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 15 (1) , 73-79
- https://doi.org/10.1017/s0004972700036777
Abstract
The following theorem is proved.Let X be a finite set of cardinality n ≥ 2, and let F be a family of subsets of X. Suppose that for F1, F2, F3 ∈ F we have |F1 ∩ F2 ∩ F3| ≥ 2. Then |F| ≤ 2n−2with equality holding if and only if for two different elements x, y of X, F = {F ⊆ X | x ∈ F, y ∈ F}.Keywords
This publication has 2 references indexed in Scilit:
- Intersection theorems for systems of finite setsActa Mathematica Hungarica, 1964
- INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETSThe Quarterly Journal of Mathematics, 1961