Combinatorica

, Volume 1, Issue 4, pp 357–368

Intersection theorems with geometric consequences

  • P. Frankl
  • R. M. Wilson
Article

DOI: 10.1007/BF02579457

Cite this article as:
Frankl, P. & Wilson, R.M. Combinatorica (1981) 1: 357. doi:10.1007/BF02579457

Abstract

In this paper we prove that if 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′ we have |FF′| ≡ μi (modp) for somei, 1 ≦is, then ||≦(sn).

As a consequence we show that ifRn is covered bym sets withm<(1+o(1)) (1.2)n then there is one set within which all the distances are realised.

It is left open whether the same conclusion holds for compositep.

AMS subject classification (1980)

05 C 6505 C 3505 C 15

Copyright information

© Akadémiai Kiadó 1981

Authors and Affiliations

  • P. Frankl
    • 1
  • R. M. Wilson
    • 2
  1. 1.C. N. R. S.ParisFrance
  2. 2.California Inst. TechnologyPasadenaU.S.A.