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About: De Bruijn sequence     Goto   Sponge   NotDistinct   Permalink

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Type: Thingyago:WikicatBinarySequencesyago:WikicatSequencesAndSeriesyago:Abstraction100002137yago:Arrangement107938773yago:Group100031264yago:Ordering108456993yago:Sequence108459252yago:Series108457976 New Facet based on Instances of this Class

In combinatorial mathematics, a de Bruijn sequence of order n on a size-k alphabet A is a cyclic sequence in which every possible length-n string on A occurs exactly once as a substring (i.e., as a contiguous subsequence). Such a sequence is denoted by B(k, n) and has length kn, which is also the number of distinct strings of length n on A. Each of these distinct strings, when taken as a substring of B(k, n), must start at a different position, because substrings starting at the same position are not distinct. Therefore, B(k, n) must have at least kn symbols. And since B(k, n) has exactly kn symbols, De Bruijn sequences are optimally short with respect to the property of containing every string of length n at least once.