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- W1484548402 abstract "Cameron and Erdős asked whether the number of emph{maximal} sum-free sets in ${1, dots , n}$ is much smaller than the number of sum-free sets. In the same paper they gave a lower bound of $2^{lfloor n/4 rfloor }$ for the number of maximal sum-free sets. Here, we prove the following: For each $1leq i leq 4$, there is a constant $C_i$ such that, given any $nequiv i mod 4$, ${1, dots , n}$ contains $(C_i+o(1)) 2^{n/4}$ maximal sum-free sets. Our proof makes use of container and removal lemmas of Green, a structural result of Deshouillers, Freiman, Sos and Temkin and a recent bound on the number of subsets of integers with small sumset by Green and Morris. We also discuss related results and open problems on the number of maximal sum-free subsets of abelian groups." @default.
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- W1484548402 date "2015-02-26" @default.
- W1484548402 modified "2023-09-27" @default.
- W1484548402 title "Sharp bound on the number of maximal sum-free subsets of integers" @default.
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