Combinatorica

, Volume 19, Issue 4, pp 555–566

Bounds on Pairs of Families with Restricted Intersections

  • Jiří Sgall
Original Paper

DOI: 10.1007/s004939970007

Cite this article as:
Sgall, J. Combinatorica (1999) 19: 555. doi:10.1007/s004939970007

such that \(\) for any \(\), \(\). We are interested in the maximum product \(\), given r and L. We give asymptotically optimal bounds for L containing only elements of s<q residue classes modulo q, where q is arbitrary (even non-prime) and s is a constant. As a consequence, we obtain a version of the Frankl–Rödl result about forbidden intersections for the case of two forbidden intersections. We also give tight bounds for L={0,...,k}.

AMS Subject Classification (1991) Classes:  05D05; 68R05

Copyright information

© János Bolyai Mathematical Society, 1999

Authors and Affiliations

  • Jiří Sgall
    • 1
  1. 1.Mathematical Institute, AS CR; Žitná 25, CZ-11567 Praha 1, Czech Republic; E-mail: sgall@math.cas.cz, http://www.math.cas.cz/~sgall/ and Dept. of Applied Mathematics, Faculty of Mathematics and Physics, Charles University; PragueCZ