Pach's animal problem within the bounding box
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914694407651328 |
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| author | Tancer, Martin |
| author_facet | Tancer, Martin |
| contents | A collection of unit cubes with integer coordinates in $\mathbb R^3$ is an animal if its union is homeomorphic to the 3-ball. Pach's animal problem asks whether any animal can be transformed to a single cube by adding or removing cubes one by one in such a way that any intermediate step is an animal as well. Here we provide an example of an animal that cannot be transformed to a single cube this way within its bounding box. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18212 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pach's animal problem within the bounding box Tancer, Martin Combinatorics 52B22 A collection of unit cubes with integer coordinates in $\mathbb R^3$ is an animal if its union is homeomorphic to the 3-ball. Pach's animal problem asks whether any animal can be transformed to a single cube by adding or removing cubes one by one in such a way that any intermediate step is an animal as well. Here we provide an example of an animal that cannot be transformed to a single cube this way within its bounding box. |
| title | Pach's animal problem within the bounding box |
| topic | Combinatorics 52B22 |
| url | https://arxiv.org/abs/2402.18212 |