Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  845.05096
Autor:  Erdös, Paul; Schönheim, J.
Title:  Sets versus divisors. (In English)
Source:  Miklós, D. (ed.) et al., Combinatorics, Paul Erdös is eighty. Vol. 2. Budapest: János Bolyai Mathematical Society, Bolyai Soc. Math. Stud. 2, 193-212 (1996).
Review:  Results on extremal families of divisors of numbers which are counterparts of known extremal set theory results are surveyed. Those properties considered include types of Sperner, Erdös-Ko-Rado, nonextendibility, restrictions on unions, intersections, inclusion, etc. Finally, a simple proof is given to a theorem of M. Geréb [On the smallest maximal sets of nonpairwise coprime divisors of a number (in Hungarian), Mat. Lapok 24, 375-380 (1973; Zbl 361.10007)].
Reviewer:  P.Komjáth (Budapest)
Classif.:  * 05D05 Extremal set theory
Keywords:  divisors of numbers; extremal set theory; Erdös-Ko-Rado; nonextendibility

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