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De Bruijn sequence
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==References== * {{cite journal |last1=van Aardenne-Ehrenfest |first1=Tanja |author-link1=Tatyana Pavlovna Ehrenfest |last2=de Bruijn |first2=Nicolaas Govert |author-link2=Nicolaas Govert de Bruijn |journal=[[Simon Stevin (journal)|Simon Stevin]] |mr=0047311 |pages=203–217 |title=Circuits and trees in oriented linear graphs |url=http://alexandria.tue.nl/repository/freearticles/597493.pdf |volume=28 |date=1951}} *{{cite journal|first1=G. K.|last1=Aguirre|first2=M. G.|last2=Mattar|first3=L.|last3=Magis-Weinberg|year=2011|url=https://cfn.upenn.edu/aguirre/wiki/public:de_bruijn|title=de Bruijn cycles for neural decoding|journal=NeuroImage|volume=56|issue=3|pages=1293–1300|doi=10.1016/j.neuroimage.2011.02.005|pmid=21315160|pmc=3104402|access-date=2015-06-04|archive-date=2016-01-26|archive-url=https://web.archive.org/web/20160126134333/https://cfn.upenn.edu/aguirre/wiki/public:de_bruijn|url-status=dead}} *{{cite web |url=http://graphics.stanford.edu/~seander/bithacks.html |title=Bit Twiddling Hacks |last=Anderson |first=Sean Eron |date=1997–2009 |publisher=[[Stanford University]] |access-date=2009-02-12}} * {{cite journal |last1=Berstel |first1=Jean |author1-link=Jean Berstel|last2=Perrin |first2=Dominique |author2-link=Dominique Perrin|doi=10.1016/j.ejc.2005.07.019 |mr=2300777 |issue=3 |journal=[[European Journal of Combinatorics]] |pages=996–1022 |title=The origins of combinatorics on words |url=http://www-igm.univ-mlv.fr/~berstel/Articles/2007Origins.pdf |volume=28 |date=2007}} *{{cite book |first=C. P. |last=Brown |author-link=C. P. Brown |date=1869 |title=Sanskrit Prosody and Numerical Symbols Explained |url=https://archive.org/stream/sanskritprosody00browgoog#page/n44/mode/2up |page=28}} * {{cite journal |last=de Bruijn |first=Nicolaas Govert |author-link=Nicolaas Govert de Bruijn |journal=Proc. Koninklijke Nederlandse Akademie V. Wetenschappen |mr=0018142 |pages=758–764 |title=A combinatorial problem |url=http://www.dwc.knaw.nl/DL/publications/PU00018235.pdf |volume=49 |date=1946 |postscript=, ''[[Indagationes Mathematicae]]'' '''8''': 461–467}} * {{cite book |last=de Bruijn |first=Nicolaas Govert |author-link=Nicolaas Govert de Bruijn |publisher=Technological University Eindhoven |series=T.H.-Report 75-WSK-06 |title=Acknowledgement of Priority to C. Flye Sainte-Marie on the counting of circular arrangements of 2<sup>n</sup> zeros and ones that show each n-letter word exactly once |url=http://alexandria.tue.nl/repository/books/252901.pdf |date=1975}} *{{cite web |url=http://7ooo.mooo.com/text/ComputingTrailingZerosHOWTO.html |title=Computing Trailing Zeros HOWTO |last=Busch |first=Philip |date=2009 |access-date=2015-01-29 |archive-date=2015-01-29 |archive-url=https://web.archive.org/web/20150129233016/http://7ooo.mooo.com/text/ComputingTrailingZerosHOWTO.html |url-status=dead }} *{{cite journal |last=Flye Sainte-Marie |first=Camille |journal=L'Intermédiaire des Mathématiciens |pages=107–110 |title=Solution to question nr. 48 |volume=1 |date=1894 }} *{{cite book |title=Algebraic Shift Register Sequences |first1=Mark |last1=Goresky|author1-link=Mark Goresky |first2=Andrew |last2=Klapper |publisher=[[Cambridge University Press]] |date=2012 |isbn=978-1-10701499-2 |pages=174–175 |url=https://books.google.com/books?id=sd9AqHeeHh4C&pg=PA174 |contribution=8.2.5 Shift register generation of de Bruijn sequences}} *{{cite journal |first=Rachel W. |last=Hall |url=http://www.sju.edu/~rhall/mathforpoets.pdf |title=Math for poets and drummers |journal=Math Horizons |volume=15 |issue=3 |date=2008 |pages=10–11 |doi=10.1080/10724117.2008.11974752 |s2cid=3637061 |access-date=2008-10-22 |archive-url=https://web.archive.org/web/20120212145748/http://www.sju.edu/~rhall/mathforpoets.pdf |archive-date=2012-02-12 |url-status=dead }} *{{cite web |url=http://www.macs.hw.ac.uk/~markl/Higgins.pdf |title=Burrows-Wheeler transforms and de Bruijn words |last=Higgins |first=Peter |date=November 2012 |access-date=2017-02-11}} * {{cite journal |last1=Hurlbert |first1=Glenn |last2=Isaak |first2=Garth |doi=10.1016/0097-3165(93)90087-O |issue=1 |journal=[[Journal of Combinatorial Theory]] |series=Series A |mr=1239511 |pages=50–62 |title=On the de Bruijn torus problem |volume=64 |date=1993 |doi-access=free }} *{{cite journal |first=Subhash |last=Kak |author-link=Subhash Kak|date=2000 |title=Yamātārājabhānasalagāṃ an interesting combinatoric sūtra |url=http://202.41.82.144/rawdataupload/upload/insa/INSA_2/200059d2_123.pdf |url-status=dead |archive-url=https://web.archive.org/web/20141029120230/http://202.41.82.144/rawdataupload/upload/insa/INSA_2/200059d2_123.pdf |archive-date=2014-10-29 |journal=Indian Journal of History of Science |volume=35 |issue=2 |pages=123–127}} *{{cite book |title=Stream Ciphers |first=Andreas |last=Klein |publisher=Springer |date=2013 |isbn=978-1-44715079-4 |page=59 |url=https://books.google.com/books?id=GYpEAAAAQBAJ&pg=PA59}} *{{Cite book |date=2006 |title=The Art of Computer Programming, Fascicle 4: Generating All Trees – History of Combinatorial Generation |first=Donald Ervin |last=Knuth |author-link=Donald Ervin Knuth |publisher=[[Addison–Wesley]] |isbn=978-0-321-33570-8 |page=50 |url=https://books.google.com/books?id=56LNfE2QGtYC&pg=PA50}} * {{cite journal |last1=Fredricksen |first1=Harold |last2=Maiorana |first2=James |doi=10.1016/0012-365X(78)90002-X |mr=523071 |issue=3 |journal=[[Discrete Mathematics (journal)|Discrete Mathematics]] |pages=207–210 |title=Necklaces of beads in ''k'' colors and ''k''-ary de Bruijn sequences |volume=23 |date=1978|doi-access=free }} *{{cite journal |last=Martin |first=Monroe H. |doi=10.1090/S0002-9904-1934-05988-3 |mr=1562989 |issue=12 |journal=[[Bulletin of the American Mathematical Society]] |pages=859–864 |title=A problem in arrangements |url=https://www.ams.org/journals/bull/1934-40-12/S0002-9904-1934-05988-3/S0002-9904-1934-05988-3.pdf |volume=40 |date=1934|doi-access=free }} * {{cite journal |last=Osipov |first=Vladimir |doi=10.1007/s10955-016-1537-5 |journal=[[Journal of Statistical Physics]] |volume=164 |issue=1 |pages=142–165 |title=Wavelet Analysis on Symbolic Sequences and Two-Fold de Bruijn Sequences |issn=1572-9613 |date=2016|arxiv=1601.02097 |bibcode=2016JSP...164..142O |s2cid=16535836 }} *{{cite book |date=2002 |orig-year=1934 |title=The logic of scientific discovery |first=Karl |last=Popper |author-link=Karl Popper |publisher=Routledge |isbn=978-0-415-27843-0 |page=294 |url=https://books.google.com/books?id=0a5bLBbe_dMC&pg=PA295}} * {{cite journal |last=Ralston |first=Anthony |doi=10.2307/2690079 |issue=3 |journal=[[Mathematics Magazine]] |mr=653429 |pages=131–143 |title=de Bruijn sequences—a model example of the interaction of discrete mathematics and computer science |volume=55 |date=1982|jstor=2690079 }} *{{cite book |first=Sherman K. |last=Stein |author-link= Sherman K. Stein |contribution=Yamátárájabhánasalagám |date=1963 |title=The Man-made Universe: An Introduction to the Spirit of Mathematics |pages=110–118}} Reprinted in Wardhaugh, Benjamin, ed. (2012), ''A Wealth of Numbers: An Anthology of 500 Years of Popular Mathematics Writing'', [[Princeton University Press]], pp. 139–144. * {{cite journal |last=Tuliani |first=Jonathan |doi=10.1016/S0012-365X(00)00117-5 |issue=1–3 |journal=[[Discrete Mathematics (journal)|Discrete Mathematics]] |mr=1802599 |pages=313–336 |title=de Bruijn sequences with efficient decoding algorithms |volume=226 |date=2001|doi-access= }} *{{cite book |title=A Course in Combinatorics |first1=J. H. |last1=van Lint|author1-link=J. H. van Lint |first2=Richard Michael |last2=Wilson|author2-link=R. M. Wilson |publisher=[[Cambridge University Press]] |date=2001 |isbn=978-0-52100601-9 |page=71 |url=https://books.google.com/books?id=5l5ps2JkyT0C&pg=PA71}}
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