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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.13640 |
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| _version_ | 1866909616880746496 |
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| author | Massé, Alexandre Blondin Goupil, Alain L'Heureux, Ralphael Marin, Louis |
| author_facet | Massé, Alexandre Blondin Goupil, Alain L'Heureux, Ralphael Marin, Louis |
| contents | Let d be an integer between 0 and 4, and W be a 2-dimensional word of dimensions h x w on the binary alphabet {0, 1}, where h, w in Z > 0. Assume that each occurrence of the letter 1 in W is adjacent to at most d letters 1. We provide an exact formula for the maximum number of letters 1 that can occur in W for fixed (h, w). As a byproduct, we deduce an upper bound on the length of maximum snake polyominoes contained in a h x w rectangle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal 2-dimensional binary words of bounded degree Massé, Alexandre Blondin Goupil, Alain L'Heureux, Ralphael Marin, Louis Combinatorics Formal Languages and Automata Theory Let d be an integer between 0 and 4, and W be a 2-dimensional word of dimensions h x w on the binary alphabet {0, 1}, where h, w in Z > 0. Assume that each occurrence of the letter 1 in W is adjacent to at most d letters 1. We provide an exact formula for the maximum number of letters 1 that can occur in W for fixed (h, w). As a byproduct, we deduce an upper bound on the length of maximum snake polyominoes contained in a h x w rectangle. |
| title | Maximal 2-dimensional binary words of bounded degree |
| topic | Combinatorics Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2505.13640 |