Journal Article10.1007/BF02579457
Intersection theorems with geometric consequences
Peter Frankl,Richard M. Wilson +1 more
594
TL;DR: It is proved that ifℱ is a family ofk-subsets of ann-set, μ0, μ1, ..., μs are distinct residues modp (p is a prime) such thatk ≡ μ0 (modp) and forF ≠ F′ ≠ℽ there is one set within which all the distances are realised.
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Abstract: In this paper we prove that ifℱ is a family ofk-subsets of ann-set, μ0, μ1, ..., μs are distinct residues modp (p is a prime) such thatk ≡ μ0 (modp) and forF ≠ F′ ≠ℱ we have |F ∩F′| ≡ μi (modp) for somei, 1 ≦i≦s, then |ℱ|≦(sn).
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References
Intersection properties of systems of finite sets
TL;DR: In this paper, a finite set of cardinality n is defined as a set of nonnegative integers with 11 enr-1 (c = e(k) is a constant depending on k).
94