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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.16621 |
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| _version_ | 1866910177991589888 |
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| author | Ivanov, Illya Strachan, Cameron |
| author_facet | Ivanov, Illya Strachan, Cameron |
| contents | Given a convex domain $C$, a $C$-polygon is an intersection of $n\geq 2$ homothets of $C$. If the homothets are translates of $C$ then we call the intersection a translative $C$-polygon. This paper proves that if $C$ is a strictly convex domain with $m$ singular boundary points, then the number of singular boundary points a $C$-polygon has is between $n$ and $2(n-1)+m$. For a translative $C$-polygon we show the number of singular boundary points is between $n$ and $n+m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16621 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Vertex Classification of Planar C-polygons Ivanov, Illya Strachan, Cameron Combinatorics Geometric Topology Given a convex domain $C$, a $C$-polygon is an intersection of $n\geq 2$ homothets of $C$. If the homothets are translates of $C$ then we call the intersection a translative $C$-polygon. This paper proves that if $C$ is a strictly convex domain with $m$ singular boundary points, then the number of singular boundary points a $C$-polygon has is between $n$ and $2(n-1)+m$. For a translative $C$-polygon we show the number of singular boundary points is between $n$ and $n+m$. |
| title | Vertex Classification of Planar C-polygons |
| topic | Combinatorics Geometric Topology |
| url | https://arxiv.org/abs/2211.16621 |