关于普通圆的数量
组合数学
2016-05-05 v2 度量几何
摘要
我们证明了任意n个不在同一直线或圆上的点至少确定1/4 n^2 - O(n)个普通圆（恰好包含其中三个点的圆）。该界的主项对于偶数n是最优的。我们的证明依赖于Green和Tao关于普通直线的一个近期结果。
引用
@article{arxiv.1412.8314,
title = {On the number of ordinary circles},
author = {Hossein Nassajian Mojarrad and Frank de Zeeuw},
journal= {arXiv preprint arXiv:1412.8314},
year = {2016}
}
备注
v2: The previous version had a mistake that turned out to be fatal to the proof. The new version has a different proof of the same result, based on the same approach, but requiring a much more detailed analysis