Negative Avoiding Sequences
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911618072313856 |
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| author | Mitchell, Chris J Wild, Peter R |
| author_facet | Mitchell, Chris J Wild, Peter R |
| contents | Negative avoiding sequences of span $n$ are periodic sequences of elements from $\mathbb{Z}_k$ for some $k$ with the property that no $n$-tuple occurs more than once in a period and if an $n$-tuple does occur then its negative does not. They are a special type of cut-down de Bruijn sequence with potential position-location applications. We establish a simple upper bound on the period of such a sequence, and refer to sequences meeting this bound as maximal negative avoiding sequences. We then go on to demonstrate the existence of maximal negative avoiding sequences for every $k\geq3$ and every $n\geq2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25286 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Negative Avoiding Sequences Mitchell, Chris J Wild, Peter R Combinatorics 05C38, 94A55 Negative avoiding sequences of span $n$ are periodic sequences of elements from $\mathbb{Z}_k$ for some $k$ with the property that no $n$-tuple occurs more than once in a period and if an $n$-tuple does occur then its negative does not. They are a special type of cut-down de Bruijn sequence with potential position-location applications. We establish a simple upper bound on the period of such a sequence, and refer to sequences meeting this bound as maximal negative avoiding sequences. We then go on to demonstrate the existence of maximal negative avoiding sequences for every $k\geq3$ and every $n\geq2$. |
| title | Negative Avoiding Sequences |
| topic | Combinatorics 05C38, 94A55 |
| url | https://arxiv.org/abs/2603.25286 |