Erdős–Fishburn triangular-lattice conjecture for few-distance configurations
Let LΔ={(a+12b,32b):a,b∈Z}L_{\Delta}=\left\{\left(a+\frac{1}{2}b,\frac{\sqrt{3}}{2}b\right):a,b\in\mathbb{Z}\right\}LΔ={(a+21b,23b):a,b∈Z} be the triangular lattice. A configuration is kkk-optimal if it has the maximum pos…