Uniqueness of Optimal Point Sets Determining Two Distinct Triangles
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866916176776396800 |
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| author | Brenner, Hazel N. Depret-Guillaume, James S. Palsson, Eyvindur A. Senger, Steven |
| author_facet | Brenner, Hazel N. Depret-Guillaume, James S. Palsson, Eyvindur A. Senger, Steven |
| contents | In this paper, we show that the maximum number of points in $d\geq3$ dimensions determining exactly 2 distinct triangles is $2d$. We further show that this maximum is uniquely achieved by the vertices of the $d$-orthoplex. We build upon the work of Hirasaka and Shinohara who determined that the $d$-orthoplex is such an optimal configuration, but did not prove its uniqueness. Further, we present a more elementary argument for its optimality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_00629 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Uniqueness of Optimal Point Sets Determining Two Distinct Triangles Brenner, Hazel N. Depret-Guillaume, James S. Palsson, Eyvindur A. Senger, Steven Combinatorics 52C10 (primary), 52C35 (secondary) In this paper, we show that the maximum number of points in $d\geq3$ dimensions determining exactly 2 distinct triangles is $2d$. We further show that this maximum is uniquely achieved by the vertices of the $d$-orthoplex. We build upon the work of Hirasaka and Shinohara who determined that the $d$-orthoplex is such an optimal configuration, but did not prove its uniqueness. Further, we present a more elementary argument for its optimality. |
| title | Uniqueness of Optimal Point Sets Determining Two Distinct Triangles |
| topic | Combinatorics 52C10 (primary), 52C35 (secondary) |
| url | https://arxiv.org/abs/1910.00629 |