Undecidability of Tiling the Plane with a Set of 5 Polyominoes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918124868075520 |
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| author | Kim, Yoonhu |
| author_facet | Kim, Yoonhu |
| contents | In this paper, we give a proof that it is undecidable whether a set of five polyominoes can tile the plane by translation. The proof involves a new method of labeling the edges of polyominoes, making it possible to assign whether two edges can match for any set of two edges chosen. This is achieved by dedicating 1 polyomino to the labeling process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10067 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Undecidability of Tiling the Plane with a Set of 5 Polyominoes Kim, Yoonhu Combinatorics 05B50 (Primary) 05B45, 52C20, 68Q17 (Secondary) In this paper, we give a proof that it is undecidable whether a set of five polyominoes can tile the plane by translation. The proof involves a new method of labeling the edges of polyominoes, making it possible to assign whether two edges can match for any set of two edges chosen. This is achieved by dedicating 1 polyomino to the labeling process. |
| title | Undecidability of Tiling the Plane with a Set of 5 Polyominoes |
| topic | Combinatorics 05B50 (Primary) 05B45, 52C20, 68Q17 (Secondary) |
| url | https://arxiv.org/abs/2508.10067 |