Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claim. The answer is yes. N. J. Calkin, On the Number of Sum-Free Sets, Bull. London Math. Soc. 22 (1990), no. 2, 141--144, proves that the number of sum-free subsets of is ; with the trivial lower bound (every subset of the integers in is sum-free) this is the displayed statement of [[problems/integer_sequences/E0748/_index|Problem 748]]. Alon proved the same bound independently (Alon 1991), and Erdős and Granville proved it in unpublished work. It is the exponent form only: the Cameron–Erdős conjecture proper, , and the two-valued asymptotic are the later theorems of Green 2003 and [[problems/integer_sequences/E0748/claims/2003_01_01_sapozhenko|Sapozhenko 2003]].
Reading. The paper is not held in this repository and was not read. Its statement is taken from the introduction of Green's paper, whose display (1) and Proposition 12 credit to Alon, Calkin and Erdős–Granville (the card green_2004_cameron_erdos_conjecture), and from the Crossref record of the DOI, which gives the venue, volume 22, issue 2, pages 141--144 and the print date of March 1990; the page name carries the first day of that month.
Acceptance. Refereed: the Bulletin of the London Mathematical Society is
a refereed journal, the refereed evidence. The site's curator credits
Green and Sapozhenko and not Calkin, so no reviewed evidence is listed.
Nothing here is this project's own review.
Depends on. No page of this wiki.