Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  215.33003
Autor:  Erdös, Paul; Komlós, J.
Title:  On a problem of Moser (In English)
Source:  Combinat. Theory Appl., Colloquia Math. Soc. Janos Bolyai 4, 365-367 (1970).
Review:  [For the entire collection see Zbl 205.00201.]
Let f(n) be the largest integer with the following property: Every family Fn of n sets contains a subfamily F'n of f(n) sets so that the union of two sets of F's never equals a third (these three sets are assumed to be pairwise different). Moser asked for the determination or estimation of f(n). A result of D.J.Kleitmann [Proc. Am. Math. Soc. 17, 139-141 (1966; Zbl 139.01004)] shows that f(n) < cn/\sqrt{log n}. J. Riddell who communicated this problem to us pointed out that f(n) > \sqrt n.
We prove the following theorem: \sqrt n \leq f(n) \leq 2 \sqrt{2n}+4.
Classif.:  * 05D05 Extremal set theory
                   05A05 Combinatorial choice problems

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