### Abstract

In this paper, upper and lower bounds each of the form c2^{n}/n^{1/4} 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| = c2^{n}/n^{1/4} + o(2^{n}/n^{1/4}) but we cannot prove this and have no guess at what the value of c is.

Original language | English |
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Pages (from-to) | 87-90 |

Number of pages | 4 |

Journal | Proceedings of the American Mathematical Society |

Volume | 28 |

Issue number | 1 |

DOIs | |

Publication status | Published - ápr. 1971 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Erdös, P., & Kleitman, D. (1971). On collections of subsets containing no 4-member boolean algebra.

*Proceedings of the American Mathematical Society*,*28*(1), 87-90. https://doi.org/10.1090/S0002-9939-1971-0270924-9