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[[FILE:LW441-MC-Escher-Moebius-Strip-II-1963.jpg|border|right|thumb|link=http://www.mcescher.com/gallery/recognition-success/mobius-strip-ii/|[[:Category:M. C. Escher|M. C. Escher]] - Möbius Strip II <ref>[http://www.mcescher.com/gallery/recognition-success/ M.C. Escher - The Official Website – Recognition & Success] </ref> <ref>[https://en.wikipedia.org/wiki/M%C3%B6bius_strip Moebius Strip from Wikipedia]</ref> ]] In [https://en.wikipedia.org/wiki/Combinatorics combinatorial mathematics], a '''k'''-ary '''De Bruijn Sequence''' B(k, n) of order '''n''', named after the Dutch mathematician [[Nicolaas de Bruijn]], is a cyclic sequence of a given alphabet '''A''' with size '''k''' for which every possible subsequence of length '''n''' in '''A''' appears as a sequence of consecutive characters exactly once <ref>[https://en.wikipedia.org/wiki/De_Bruijn_sequence De Bruijn sequence from Wikipedia]</ref>. In chess programming there are applications of de Bruijn sequences with the Binary alphabet, in [[Hash Table|hashing]] sets like [[Piece-Sets]] or Square-sets, also called [[Bitboards]], most notably in [[BitScan#DeBruijnMultiplation|Bit scanning]] <ref>[[Charles Leiserson|Charles E. Leiserson]], [[Harald Prokop]], [[Keith H. Randall]] ('''1998'''). ''Using de Bruijn Sequences to Index a 1 in a Computer Word''. [http://supertech.csail.mit.edu/papers/debruijn.pdf pdf]</ref> .
=Binary alphabet=
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