A Carousel Property for Compact Convex Sets
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909966652145664 |
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| author | Song, Yiming |
| author_facet | Song, Yiming |
| contents | We prove that if $A_0$ and $A_1$ are compact convex sets contained in a convex $n$-gon with vertices $g_1, \dots, g_n$, and $n$ is strictly greater than the number of common supporting lines of $A_0$ and $A_1$, then there exist $i \in \{0,1\}$ and $j \in \{1,\dots, n\}$ such that $A_i$ is in the convex hull of $A_{1-i}$ and $(\{g_1, \dots, g_n\} \setminus \{g_j\})$. This recovers and generalizes previous results of Adaricheva--Bolat and Cz{é}dli. We also show that this bound is sharp for even $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14972 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Carousel Property for Compact Convex Sets Song, Yiming Combinatorics 52C07 (Primary), 52C35 (Secondary) We prove that if $A_0$ and $A_1$ are compact convex sets contained in a convex $n$-gon with vertices $g_1, \dots, g_n$, and $n$ is strictly greater than the number of common supporting lines of $A_0$ and $A_1$, then there exist $i \in \{0,1\}$ and $j \in \{1,\dots, n\}$ such that $A_i$ is in the convex hull of $A_{1-i}$ and $(\{g_1, \dots, g_n\} \setminus \{g_j\})$. This recovers and generalizes previous results of Adaricheva--Bolat and Cz{é}dli. We also show that this bound is sharp for even $n$. |
| title | A Carousel Property for Compact Convex Sets |
| topic | Combinatorics 52C07 (Primary), 52C35 (Secondary) |
| url | https://arxiv.org/abs/2512.14972 |