We investigate the Gerver-Ramsey collinearity problem of determining the maximum number of points in a north-east lattice path without $k$ collinear points. Using a satisfiability solver, up to isomorphism we enumerate all north-east lattice paths avoiding $k$ collinear points for $k \leq 6$. We also find a north-east lattice path avoiding $k = 7$ collinear points with 327 steps, improving on the previous best length of 260 steps found by Shallit.

翻译：我们研究了Gerver-Ramsey共线性问题，即确定东北格点路径中无$k$个共线点的最大点数。通过使用可满足性求解器，我们在同构意义下枚举了所有避免$k \leq 6$个共线点的东北格点路径。此外，我们发现了一条避免$k = 7$个共线点、步长为327的东北格点路径，改进了Shallit此前发现的260步的最优长度。