Enumeration of Polyominoes up to Size N=59
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914115250814976 |
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| author | Shirakawa, Toshihiro |
| author_facet | Shirakawa, Toshihiro |
| contents | This paper reports the results of numerical computations for determining the number of polyominoes of size n (n-ominoes). We verify the existing counts for n <= 50 and newly compute the total number of polyominoes up to n <= 59, extending the counting limit. This work shows that, in addition to optimizing the search algorithm for the polyomino counting problem, multi-threading dramatically improves computational efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enumeration of Polyominoes up to Size N=59 Shirakawa, Toshihiro Combinatorics Discrete Mathematics 05B50 F.2.2; G.2.1 This paper reports the results of numerical computations for determining the number of polyominoes of size n (n-ominoes). We verify the existing counts for n <= 50 and newly compute the total number of polyominoes up to n <= 59, extending the counting limit. This work shows that, in addition to optimizing the search algorithm for the polyomino counting problem, multi-threading dramatically improves computational efficiency. |
| title | Enumeration of Polyominoes up to Size N=59 |
| topic | Combinatorics Discrete Mathematics 05B50 F.2.2; G.2.1 |
| url | https://arxiv.org/abs/2510.22446 |