On collections of subsets containing no 4-member boolean algebra

Paul Erdös, Daniel Kleitman

Research output: Article

9 Citations (Scopus)


In this paper, upper and lower bounds each of the form c2n/n1/4 are obtained for the maximum possible size of a collection Q of subsets of an n element set satisfying the restriction that no four distinct members A, B, C, D of Q satisfy A ∪ B = C and A ∩ B = D. The lower bound is obtained by a construction while the upper bound is obtained by applying a somewhat weaker condition on Q which leads easily to a bound. Probably there is an absolute constant c so that max|Q| = c2n/n1/4 + o(2n/n1/4) but we cannot prove this and have no guess at what the value of c is.

Original languageEnglish
Pages (from-to)87-90
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number1
Publication statusPublished - ápr. 1971

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'On collections of subsets containing no 4-member boolean algebra'. Together they form a unique fingerprint.

  • Cite this