North-East Lattice Paths Avoiding $k$ Collinear Points via Satisfiability
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910224184508416 |
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| author | Barnoff, Aaron Bright, Curtis |
| author_facet | Barnoff, Aaron Bright, Curtis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23226 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | North-East Lattice Paths Avoiding $k$ Collinear Points via Satisfiability Barnoff, Aaron Bright, Curtis Combinatorics Discrete Mathematics Logic in Computer Science 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. |
| title | North-East Lattice Paths Avoiding $k$ Collinear Points via Satisfiability |
| topic | Combinatorics Discrete Mathematics Logic in Computer Science |
| url | https://arxiv.org/abs/2511.23226 |