Constructions of Large m-Distance Sets on Triangular Lattice
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908512061227008 |
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| author | Bao, Li-Ren Yu, Wei-Hsuan |
| author_facet | Bao, Li-Ren Yu, Wei-Hsuan |
| contents | An $m$-distance set is a collection of points such that the distances between any two points have $m$ possible values. We use two different methods to construct large $m$-distance sets on the triangular lattices. One is to use the first m smallest distances and find the largest cliques, and the other is using the notions of hexagons. Multiplicities of the distances were observed for comparison for the two methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructions of Large m-Distance Sets on Triangular Lattice Bao, Li-Ren Yu, Wei-Hsuan Combinatorics Metric Geometry An $m$-distance set is a collection of points such that the distances between any two points have $m$ possible values. We use two different methods to construct large $m$-distance sets on the triangular lattices. One is to use the first m smallest distances and find the largest cliques, and the other is using the notions of hexagons. Multiplicities of the distances were observed for comparison for the two methods. |
| title | Constructions of Large m-Distance Sets on Triangular Lattice |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2509.00880 |