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arXiv · 2511.23226

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

Aaron Barnoff·Curtis Bright
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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.

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BibTeXRIS

Aaron Barnoff, Curtis Bright. 2026-05-04. North-East Lattice Paths Avoiding $k$ Collinear Points via Satisfiability. https://doi.org/10.1016/j.aam.2026.103112

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