North-East Lattice Paths Avoiding $k$ Collinear Points via Satisfiability

Abstract

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.