On the number of generalized Sidon sets

@article{Balogh2018OnTN,
  title={On the number of generalized Sidon sets},
  author={J{\'o}zsef Balogh and Lina Li},
  journal={arXiv: Combinatorics},
  year={2018}
}
A set $A$ of nonnegative integers is called a Sidon set if there is no Sidon 4-tuple, i.e., $(a,b,c,d)$ in $A$ with $a+b=c+d$ and $\{a, b\}\cap \{c, d\}=\emptyset$. Cameron and Erd\H os proposed the problem of determining the number of Sidon sets in $[n]$. Results of Kohayakawa, Lee, R\" odl and Samotij, and Saxton and Thomason has established that the number of Sidon sets is between $2^{(1.16+o(1))\sqrt{n}}$ and $2^{(6.442+o(1))\sqrt{n}}$. An $\alpha$-generalized Sidon set in $[n]$ is a set… 
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