de Bruijn sequence

E239166

A de Bruijn sequence is a cyclic sequence over a given alphabet in which every possible subsequence of a fixed length appears exactly once.

All labels observed (2)

Label Occurrences
de Bruijn sequence canonical 3
de Bruijn cycle 1

How this entity was disambiguated

Statements (48)

Predicate Object
instanceOf combinatorial object
cyclic sequence
sequence
alsoKnownAs de Bruijn sequence
surface form: de Bruijn cycle
application efficiently encoding all possible patterns of fixed length
minimizing sequence length while covering all fixed-length substrings
constructionMethod finding an Eulerian cycle in a de Bruijn graph of order n
using Lyndon words concatenation (Fredricksen–Maiorana construction)
using linear feedback shift registers for certain parameters
definition a cyclic sequence over a given alphabet in which every possible subsequence of a fixed length appears exactly once
example 00010111 is a binary de Bruijn sequence of order 3
field combinatorics
discrete mathematics
hasProperty any reflection of a de Bruijn sequence over a symmetric alphabet is also a de Bruijn sequence
any rotation of a de Bruijn sequence is also a de Bruijn sequence
binary de Bruijn sequence has alphabet size 2
binary de Bruijn sequence of order n has length 2^n
contains every possible length-n word over an alphabet of size k exactly once as a contiguous subsequence
defined for any finite alphabet
is a Hamiltonian cycle in the de Bruijn graph
is a minimal-length sequence containing all k-ary strings of length n as substrings
is cyclic so that subsequences can wrap around the end to the beginning
is periodic with period k^n
maximizes substring diversity for a given length and alphabet
number of distinct de Bruijn sequences grows rapidly with k and n
sequence length equals k^n for alphabet size k and subsequence length n
subsequences are usually considered as contiguous substrings
namedAfter N. G. de Bruijn
surface form: Nicolaas Govert de Bruijn
parameter alphabet size
subsequence length
relatedTo Eulerian cycle
Gray code
combinatorial design
de Bruijn graph
Pólya enumeration theorem
surface form: necklace (combinatorics)

shift register sequence
universal cycle
word (combinatorics)
specialCaseOf universal cycle for k-ary strings of length n
typicalNotation B(k,n)
usedIn DNA sequencing and assembly algorithms
Coding Theory
surface form: coding theory

cryptography
design of experiments
hardware testing
keyboard and input device testing
pseudorandom number generation
robot motion planning

How these facts were elicited

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

N. G. de Bruijn notableWork de Bruijn sequence
de Bruijn sequence alsoKnownAs de Bruijn sequence
this entity surface form: de Bruijn cycle
de Bruijn graph relatedTo de Bruijn sequence