Generalizations of cyclic polytopes
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913352133902336 |
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| author | Bisztriczky, Tibor |
| author_facet | Bisztriczky, Tibor |
| contents | Cyclic polytopes have been studied since at least the early last century by Caratheodory and others.A generalization is a construction of a class of polytopes such that the polytopes have some of their properties.The best known example is the class of neighbourly polytopes. Cyclic polytopes have explicit facet structures, important properties and applications in different branches of mathematics. In the past few decades, generalizations of their combinatorial properties have yielded new classes of polytopes that also have explicit facet structures and useful applications. We present an overview of these generalizations along with some applications of the resultant polytopes, and some possible approaches to other generalizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09429 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalizations of cyclic polytopes Bisztriczky, Tibor Combinatorics Metric Geometry Primary: 52B12, 52-02. Secondary: 52B05, 52B11, 52C07 Cyclic polytopes have been studied since at least the early last century by Caratheodory and others.A generalization is a construction of a class of polytopes such that the polytopes have some of their properties.The best known example is the class of neighbourly polytopes. Cyclic polytopes have explicit facet structures, important properties and applications in different branches of mathematics. In the past few decades, generalizations of their combinatorial properties have yielded new classes of polytopes that also have explicit facet structures and useful applications. We present an overview of these generalizations along with some applications of the resultant polytopes, and some possible approaches to other generalizations. |
| title | Generalizations of cyclic polytopes |
| topic | Combinatorics Metric Geometry Primary: 52B12, 52-02. Secondary: 52B05, 52B11, 52C07 |
| url | https://arxiv.org/abs/2405.09429 |