Counting Sets of Integers with Various Summation Properties

Derek Jennings

A chapter in Applications of Fibonacci Numbers, 1996, pp 271-281 from Springer

Abstract: Abstract The motivation behind these investigations comes form a problem due to P.J. Cameron and P. Erdös, presented at the Fourteenth British Combinatorial Conference (1993) [1, 2]. They conjectured that $$ \frac{{S\left( s \right)}}{{{2^{n/2}}}} \to {C_0} or {C_E} $$ (for constants C 0 and C E ), as n→∞ through odd or even values respectively, where S(n) is the number of sum-free subsets of the first n natural numbers (i.e. containing no solution to x + y = z, where x and y are not necessarily distinct).

Date: 1996
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DOI: 10.1007/978-94-009-0223-7_22

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