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

Combinatorics 2026-05-19 v2 Discrete Mathematics Logic in Computer Science

Abstract

We investigate the Gerver-Ramsey collinearity problem of determining the maximum number of points in a north-east lattice path without kk collinear points. Using a satisfiability solver, up to isomorphism we enumerate all north-east lattice paths avoiding kk collinear points for k6k \leq 6. We also find a north-east lattice path avoiding k=7k = 7 collinear points with 327 steps, improving on the previous best length of 260 steps found by Shallit.

Cite

@article{arxiv.2511.23226,
  title  = {North-East Lattice Paths Avoiding $k$ Collinear Points via Satisfiability},
  author = {Aaron Barnoff and Curtis Bright},
  journal= {arXiv preprint arXiv:2511.23226},
  year   = {2026}
}

Comments

To appear in Advances in Applied Mathematics

R2 v1 2026-07-01T07:59:30.142Z