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Almost Odd Random Sum-Free Sets

Published online by Cambridge University Press:  01 March 1998

NEIL J. CALKIN  and
P. J. CAMERON
NEIL J. CALKIN
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA (e-mail: [email protected])
P. J. CAMERON
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, London E1 4NS, UK (e-mail: [email protected])
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Abstract

We show that if S1 is a strongly complete sum-free set of positive integers, and if S0 is a finite sum-free set, then, with positive probability, a random sum-free set U contains S0 and is contained in S0∪S1. As a corollary we show that, with positive probability, 2 is the only even element of a random sum-free set.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 7 , Issue 1 , March 1998 , pp. 27 - 32
Copyright
1998 Cambridge University Press

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