Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  838.11018
Autor:  Alon, Noga; Erdös, Paul
Title:  Sure monochromatic subset sums. (In English)
Source:  Acta Arith. 74, No.3, 269-272 (1996).
Review:  Let f(n) denote the smallest integer f such that one can color the integers {1, 2, ...,n-1} by f colors so that there is no monochromatic subset the sum of whose elements is n. It is shown that

\Omega ({{n1/3} \over {log4/3 n}}) \leq f(n) \leq O({{n1/3 (log log n)1/3} \over {log1/3 n}}).

The lower bound settles a problem of Erdös.
Reviewer:  N.Alon (Tel Aviv)
Classif.:  * 11B75 Combinatorial number theory
                   11N36 Appl. of sieve methods
Keywords:  subset sums; Brun's sieve; monochromatic subset

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