On collections of subsets containing no 4-member boolean algebra

Paul Erdös, Daniel Kleitman

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9 Citations (Scopus)

Abstract

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
Volume28
Issue number1
DOIs
Publication statusPublished - Apr 1971

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Keywords

  • Bounds on collection size
  • Sizes of subset families

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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