Convex fair partitions into an arbitrary number of pieces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866911541984493568 |
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| author | Akopyan, Arseniy Avvakumov, Sergey Karasev, Roman |
| author_facet | Akopyan, Arseniy Avvakumov, Sergey Karasev, Roman |
| contents | We prove that any convex body in the plane can be partitioned into $m$ convex parts of equal areas and perimeters for any integer $m\ge 2$; this result was previously known for prime powers $m=p^k$. We also discuss possible higher-dimensional generalizations and difficulties of extending our technique to equalizing more than one non-additive function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1804_03057 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Convex fair partitions into an arbitrary number of pieces Akopyan, Arseniy Avvakumov, Sergey Karasev, Roman Metric Geometry Algebraic Topology Combinatorics 51F99, 52C35, 55M20, 55M35 We prove that any convex body in the plane can be partitioned into $m$ convex parts of equal areas and perimeters for any integer $m\ge 2$; this result was previously known for prime powers $m=p^k$. We also discuss possible higher-dimensional generalizations and difficulties of extending our technique to equalizing more than one non-additive function. |
| title | Convex fair partitions into an arbitrary number of pieces |
| topic | Metric Geometry Algebraic Topology Combinatorics 51F99, 52C35, 55M20, 55M35 |
| url | https://arxiv.org/abs/1804.03057 |