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 ≤ 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.
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