On the characteristic and diameter of planar integral point sets
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918248477360128 |
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| author | Avdeev, N. N. Lushina, E. A. |
| author_facet | Avdeev, N. N. Lushina, E. A. |
| contents | A point set $M$ in Euclidean plane is called an integral point set in semi-general position if all the distances between the elements of $M$ are integers, and $M$ does not contain collinear triples. We improve the lower bound for diameter of such sets in the particular case when the characteristic of the set is of the form $4k+1$ or $4k+2$. To achieve that, we combine hyperbolae-based and grid-based toolsets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the characteristic and diameter of planar integral point sets Avdeev, N. N. Lushina, E. A. Combinatorics Algebraic Geometry A point set $M$ in Euclidean plane is called an integral point set in semi-general position if all the distances between the elements of $M$ are integers, and $M$ does not contain collinear triples. We improve the lower bound for diameter of such sets in the particular case when the characteristic of the set is of the form $4k+1$ or $4k+2$. To achieve that, we combine hyperbolae-based and grid-based toolsets. |
| title | On the characteristic and diameter of planar integral point sets |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2407.08121 |