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arXiv · 2603.25286

Negative Avoiding Sequences

Chris J Mitchell·Peter R Wild
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Abstract

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 $n\geq2$.

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Chris J Mitchell, Peter R Wild. 2026-04-23. Negative Avoiding Sequences. https://arxiv.org/abs/2603.25286

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