Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 742.11008
Autor: Erdös, Paul; Nicolas, J.-L.; Sárközy, A.
Title: Sommes de sous-ensembles. (Subset sums.) (In French)
Source: Sémin. Théor. Nombres Bordx., Sér. II 3, No.1, 55-72 (1991).
Review: For any set A\subseteqN let P(A,k) be the set of all n which are expressible as sums of exactly k distinct elements of A. The set A is called admissible if, for k\ne\ell, P(A,k)\capP(A,\ell) = 0. The autors prove that, if F(N) is the maximal cardinality of admissible sets A\subseteq{1,...,N}, then limsupN ––> ooF(N)N- ½ ––> (143/27) ½, thereby slightly sharpening a result due to E. G. Straus [J. Math. Sci. 1, 77-80 (1966; Zbl 149.28503)]. The paper also contains a result on infinite admissible sets and some general conjectures.
Reviewer: B.Volkmann (Stuttgart)
Classif.: * 11B13 Additive bases
Keywords: maximal cardinality; admissible sets; infinite admissible sets
Citations: Zbl 149.285
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