T-Tetrominos in Arithmetic Progression
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910314887380992 |
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| author | Feller, Emily Hochberg, Robert |
| author_facet | Feller, Emily Hochberg, Robert |
| contents | A famous result of D. Walkup is that an $m\times n$ rectangle may be tiled by T-tetrominos if and only if both $m$ and $n$ are multiples of 4. The "if" portion may be proved by tiling a $4\times 4$ block, and then copying that block to fill the rectangle; but, this leads to regular, periodic tilings. In this paper we investigate how much "order" must be present in every tiling of a rectangle by T-tetrominos, where we measure order by length of arithmetic progressions of tiles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_00533 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | T-Tetrominos in Arithmetic Progression Feller, Emily Hochberg, Robert Combinatorics 05D10, 05B45 A famous result of D. Walkup is that an $m\times n$ rectangle may be tiled by T-tetrominos if and only if both $m$ and $n$ are multiples of 4. The "if" portion may be proved by tiling a $4\times 4$ block, and then copying that block to fill the rectangle; but, this leads to regular, periodic tilings. In this paper we investigate how much "order" must be present in every tiling of a rectangle by T-tetrominos, where we measure order by length of arithmetic progressions of tiles. |
| title | T-Tetrominos in Arithmetic Progression |
| topic | Combinatorics 05D10, 05B45 |
| url | https://arxiv.org/abs/2207.00533 |