On lattice triangles satisfying $\boldsymbol{B(T)=3}$ with collinear interior lattice points
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915120883433472 |
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| author | Li, Eddy Paquin, Dana |
| author_facet | Li, Eddy Paquin, Dana |
| contents | A lattice point in $\mathbb{R}^2$ is a point $(x,y)$ with $x,y\in\mathbb{Z}$, and a lattice triangle is a triangle whose three vertices are all lattice points. We investigate the integers $k$ with the property that if $T$ is a lattice triangle with $3$ boundary points and $k$ points in the interior, then all $k$ boundary points must be collinear. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On lattice triangles satisfying $\boldsymbol{B(T)=3}$ with collinear interior lattice points Li, Eddy Paquin, Dana Combinatorics 52A10, 52C05, 11H06 A lattice point in $\mathbb{R}^2$ is a point $(x,y)$ with $x,y\in\mathbb{Z}$, and a lattice triangle is a triangle whose three vertices are all lattice points. We investigate the integers $k$ with the property that if $T$ is a lattice triangle with $3$ boundary points and $k$ points in the interior, then all $k$ boundary points must be collinear. |
| title | On lattice triangles satisfying $\boldsymbol{B(T)=3}$ with collinear interior lattice points |
| topic | Combinatorics 52A10, 52C05, 11H06 |
| url | https://arxiv.org/abs/2501.15009 |