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On the Density of Universal Sum-Free Sets

Published online by Cambridge University Press:  01 May 1999

TOMASZ SCHOEN
TOMASZ SCHOEN
Affiliation:
Department of Discrete Mathematics, Adam Mickiewicz University, Poznán, Poland (e-mail: schoen@math.amu.edu.pl)
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Abstract

A set A is called universal sum-free if, for every finite 0–1 sequence χ = (e1, …, en), either

(i) there exist i, j, where 1[les ]j<i[les ]n, such that ei = ej = 1 and i − j∈A, or

(ii) there exists t∈N such that, for 1[les ]i[les ]n, we have t + i∈A if and only if ei = 1.

It is proved that the density of each universal sum-free set is zero, which settles a problem of Cameron.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 8 , Issue 3 , May 1999 , pp. 277 - 280
Copyright
1999 Cambridge University Press

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