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
This entity first appeared as the object of triple T2169626 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: de Bruijn sequence Context triple: [N. G. de Bruijn, notableWork, de Bruijn sequence]
-
A.
Look-and-say sequence
The look-and-say sequence is a famous integer sequence where each term is generated by verbally describing the digits of the previous term, studied for its surprising combinatorial and growth properties.
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B.
Berlekamp–Massey algorithm
The Berlekamp–Massey algorithm is a key algorithm in coding theory and cryptography used to efficiently determine the shortest linear feedback shift register that generates a given binary sequence.
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C.
Ulam sequence
The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
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D.
Alexander–Briggs notation
Alexander–Briggs notation is a classical system for naming and classifying knots in knot theory, assigning each distinct knot a unique label based on its crossing number and order in knot tables.
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E.
Knuth–Morris–Pratt algorithm
The Knuth–Morris–Pratt algorithm is a classic linear-time string-searching algorithm that efficiently finds occurrences of a pattern within a text by precomputing a prefix function to avoid redundant comparisons.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: de Bruijn sequence Target entity description: A de Bruijn sequence is a cyclic sequence over a given alphabet in which every possible subsequence of a fixed length appears exactly once.
-
A.
Look-and-say sequence
The look-and-say sequence is a famous integer sequence where each term is generated by verbally describing the digits of the previous term, studied for its surprising combinatorial and growth properties.
-
B.
Berlekamp–Massey algorithm
The Berlekamp–Massey algorithm is a key algorithm in coding theory and cryptography used to efficiently determine the shortest linear feedback shift register that generates a given binary sequence.
-
C.
Ulam sequence
The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
-
D.
Alexander–Briggs notation
Alexander–Briggs notation is a classical system for naming and classifying knots in knot theory, assigning each distinct knot a unique label based on its crossing number and order in knot tables.
-
E.
Knuth–Morris–Pratt algorithm
The Knuth–Morris–Pratt algorithm is a classic linear-time string-searching algorithm that efficiently finds occurrences of a pattern within a text by precomputing a prefix function to avoid redundant comparisons.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial object
ⓘ
cyclic sequence ⓘ sequence ⓘ |
| alsoKnownAs |
de Bruijn cycle
ⓘ
linked to:
de Bruijn sequence
|
| 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 |
Nicolaas Govert de Bruijn
ⓘ
linked to:
N. G. de Bruijn
|
| parameter |
alphabet size
ⓘ
subsequence length ⓘ |
| relatedTo |
Eulerian cycle
ⓘ
Gray code ⓘ combinatorial design ⓘ de Bruijn graph ⓘ necklace (combinatorics) ⓘ
linked to:
Pólya enumeration theorem
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 ⓘ
linked to:
Coding Theory
cryptography ⓘ design of experiments ⓘ hardware testing ⓘ keyboard and input device testing ⓘ pseudorandom number generation ⓘ robot motion planning ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: de Bruijn sequence Description of subject: A de Bruijn sequence is a cyclic sequence over a given alphabet in which every possible subsequence of a fixed length appears exactly once.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: de Bruijn sequence