Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

On Collections of Subsets Containing No 4-Member Boolean Algebra

Paul Erdös and Daniel Kleitman
Proceedings of the American Mathematical Society
Vol. 28, No. 1 (Apr., 1971), pp. 87-90
DOI: 10.2307/2037762
Stable URL: http://www.jstor.org/stable/2037762
Page Count: 4
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
On Collections of Subsets Containing No 4-Member Boolean Algebra
Preview not available

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 $A \cup B = C$ and $A \cap B = D$. 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.

Page Thumbnails

  • Thumbnail: Page 
87
    87
  • Thumbnail: Page 
88
    88
  • Thumbnail: Page 
89
    89
  • Thumbnail: Page 
90
    90