Sidon set density inside (4,5) sets
Description of constant
$C_{5b}$ is the largest constant such that every $(4,5)$-set of size $n$ (i.e., a set of reals such that every four-element subset determines at least five distinct differences) contains a Sidon set of cardinality $C_{5b}n$.
Known upper bounds
| Bound |
Reference |
Comments |
| $1$ |
Trivial |
|
| $\frac{3}{5} = 0.6$ |
[GL95] |
|
| $\frac{4}{7} \approx 0.5714$ |
[MT26] |
|
Known lower bounds
| Bound |
Reference |
Comments |
| $\frac{1}{2}$ |
[GL95] |
A short 2-colorability argument |
| $\frac{1}{2} + \frac{1}{141 \times 76} \approx 0.500093$ |
[GL95] |
|
| $\frac{9}{17} \approx 0.5294$ |
[MT26] |
|
References
- [GL95] A. Gyárfás and J. Lehel, Linear sets with five distinct differences among any four elements, J. Combin. Theory Ser. B 64 (1995), 108–118.
- [MT26] Jie Ma and Quanyu Tang, Largest Sidon subsets in weak Sidon sets. arXiv:2602.23282 (2026).