On the classification of lattice polytopes via affine equivalence
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909317271126016 |
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| author | Cai, Zhanyuan Zhang, Yuqin Liu, Qiuyue |
| author_facet | Cai, Zhanyuan Zhang, Yuqin Liu, Qiuyue |
| contents | In 1980, V. I. Arnold studied the classification problem for convex lattice polygons of a given area. Since then, this problem and its analogues have been studied by many authors, including Bárány, Lagarias, Pach, Santos, Ziegler and Zong. Despite extensive study, the structure of the representative sets in the classifications remains unclear, indicating a need for refined classification methods. In this paper, we propose a novel classification framework based on affine equivalence, which offers a fresh perspective on the problem. Our approach yields several classification results that extend and complement Bárány's work on volume and Zong's work on cardinality. These new results provide a more nuanced understanding of the structure of the representative set, offering deeper insights into the classification problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09985 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the classification of lattice polytopes via affine equivalence Cai, Zhanyuan Zhang, Yuqin Liu, Qiuyue Metric Geometry 52B20, 52C07 In 1980, V. I. Arnold studied the classification problem for convex lattice polygons of a given area. Since then, this problem and its analogues have been studied by many authors, including Bárány, Lagarias, Pach, Santos, Ziegler and Zong. Despite extensive study, the structure of the representative sets in the classifications remains unclear, indicating a need for refined classification methods. In this paper, we propose a novel classification framework based on affine equivalence, which offers a fresh perspective on the problem. Our approach yields several classification results that extend and complement Bárány's work on volume and Zong's work on cardinality. These new results provide a more nuanced understanding of the structure of the representative set, offering deeper insights into the classification problem. |
| title | On the classification of lattice polytopes via affine equivalence |
| topic | Metric Geometry 52B20, 52C07 |
| url | https://arxiv.org/abs/2409.09985 |