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arXiv · 1608.08480

An Unoriented Variation on de Bruijn Sequences

Christie S. Burris·Francis C. Motta·Patrick D. Shipman
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Abstract

For positive integers $k,n$, a de Bruijn sequence $B(k,n)$ is a finite sequence of elements drawn from $k$ characters whose subwords of length $n$ are exactly the $k^n$ words of length $n$ on $k$ characters. This paper introduces the unoriented de Bruijn sequence $uB(k,n)$, an analog to de Bruijn sequences, but for which the sequence is read both forwards and backwards to determine the set of subwords of length $n$. We show that nontrivial unoriented de Bruijn sequences of optimal length exist if and only if $k$ is two or odd and $n$ is less than or equal to 3. Unoriented de Bruijn sequences for any $k$, $n$ may be constructed from certain Eulerian paths in Eulerizations of unoriented de Bruijn graphs.

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Christie S. Burris, Francis C. Motta, Patrick D. Shipman. 2016-08-30. An Unoriented Variation on de Bruijn Sequences. https://arxiv.org/abs/1608.08480

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