Counting tilings of the $n \times m$ grid, cylinder, and torus
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912613621825536 |
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| author | Kagey, Peter Keehn, William |
| author_facet | Kagey, Peter Keehn, William |
| contents | We count tilings of the $n \times m$ rectangular grid, cylinder, and torus with arbitrary tile sets up to arbitrary symmetries of the square and rectangle, along with cyclic shifting of rows and columns. This provides a unifying framework for understanding a family of counting problems, expanding on the work by Ethier and Lee counting tilings of the torus by tiles of two colors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13072 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Counting tilings of the $n \times m$ grid, cylinder, and torus Kagey, Peter Keehn, William Combinatorics Group Theory 05A05 We count tilings of the $n \times m$ rectangular grid, cylinder, and torus with arbitrary tile sets up to arbitrary symmetries of the square and rectangle, along with cyclic shifting of rows and columns. This provides a unifying framework for understanding a family of counting problems, expanding on the work by Ethier and Lee counting tilings of the torus by tiles of two colors. |
| title | Counting tilings of the $n \times m$ grid, cylinder, and torus |
| topic | Combinatorics Group Theory 05A05 |
| url | https://arxiv.org/abs/2311.13072 |