Universal partial tori
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913768928182272 |
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| author | Carey, William D. Kearney, Matthew David Kirsch, Rachel Popescu, Stefan |
| author_facet | Carey, William D. Kearney, Matthew David Kirsch, Rachel Popescu, Stefan |
| contents | A De Bruijn cycle is a cyclic sequence in which every word of length $n$ over an alphabet $\mathcal{A}$ appears exactly once. De Bruijn tori are a two-dimensional analogue. Motivated by recent progress on universal partial cycles and words, which shorten De Bruijn cycles using a wildcard character, we introduce universal partial tori and matrices. We find them computationally and construct infinitely many of them using one-dimensional variants of universal cycles, including a new variant called a universal partial family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12417 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal partial tori Carey, William D. Kearney, Matthew David Kirsch, Rachel Popescu, Stefan Combinatorics Discrete Mathematics 68R15, 05B30 A De Bruijn cycle is a cyclic sequence in which every word of length $n$ over an alphabet $\mathcal{A}$ appears exactly once. De Bruijn tori are a two-dimensional analogue. Motivated by recent progress on universal partial cycles and words, which shorten De Bruijn cycles using a wildcard character, we introduce universal partial tori and matrices. We find them computationally and construct infinitely many of them using one-dimensional variants of universal cycles, including a new variant called a universal partial family. |
| title | Universal partial tori |
| topic | Combinatorics Discrete Mathematics 68R15, 05B30 |
| url | https://arxiv.org/abs/2409.12417 |