On collections of subsets containing no 4-member boolean algebra

P. Erdős, Daniel Kleitman

Research output: Contribution to journalArticle

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 language English 87-90 4 Proceedings of the American Mathematical Society 28 1 https://doi.org/10.1090/S0002-9939-1971-0270924-9 Published - 1971

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Boolean algebra
Guess
Set theory
Upper and Lower Bounds
Lower bound
Upper bound
Restriction
Distinct
Subset
Form

Keywords

• Bounds on collection size
• Sizes of subset families

ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics

Cite this

On collections of subsets containing no 4-member boolean algebra. / Erdős, P.; Kleitman, Daniel.

In: Proceedings of the American Mathematical Society, Vol. 28, No. 1, 1971, p. 87-90.

Research output: Contribution to journalArticle

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