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 collinear points. Using a satisfiability solver, up to isomorphism we enumerate all north-east lattice paths avoiding collinear points for . We also find a north-east lattice path avoiding 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