On extending de Bruijn sequences

We give a complete proof of the following theorem: Every de Bruijn sequence of order n in at least three symbols can be extended to a de Bruijn sequence of order n + 1 . Every de Bruijn sequence of order n in two symbols can not be extended to order n + 1 , but it can be extended to order n + 2 . ►...

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Veröffentlicht in:	Information processing letters 2011-09, Vol.111 (18), p.930-932
Hauptverfasser:	Becher, Verónica, Heiber, Pablo Ariel
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithmics. Computability. Computer arithmetics Applied sciences Combinatorial problems Computer science control theory systems De Bruijn sequences Exact sciences and technology Graph algorithms Mathematical analysis Miscellaneous Proof theory Studies Theorems Theoretical computing Word problems
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Beschreibung
Zusammenfassung:	We give a complete proof of the following theorem: Every de Bruijn sequence of order n in at least three symbols can be extended to a de Bruijn sequence of order n + 1 . Every de Bruijn sequence of order n in two symbols can not be extended to order n + 1 , but it can be extended to order n + 2 . ► De Bruijn sequences in at least three symbols can be extended to the next order. ► De Bruijn sequences in two symbols can not be extended to the next order. ► De Bruijn sequences in two symbols can be extended to two orders ahead.
ISSN:	0020-0190 1872-6119
DOI:	10.1016/j.ipl.2011.06.013