Union-free families of sets and equations over fields

P. Frankl, Z. Füredi

Research output: Contribution to journalArticle

11 Citations (Scopus)


Let X be an n-element set and F ⊂ (k x) such that all the (2 |F|) sets F1 {smile} F2, F1, F2 ∈ F are distinct. Solving a problem of P. Erdo{combining double acute accent}s ("Proceedings, 8th Southeastern Conf. on Combinatorics, Graph Theory, and Computing, Baton Rouge, 1977", pp.3-12) we show that there exist positive constants ck, c′k such that ckn⌈4k/3⌉/2≤|F|≤c′k n⌈4k/3⌉/2 holds. For the proof of the lower bound we need a theorem of independent interest which is of algebraic number-theoretic character (Theorem 1.4.).

Original languageEnglish
Pages (from-to)210-218
Number of pages9
JournalJournal of Number Theory
Issue number2
Publication statusPublished - Jun 1986


ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this