de Bruijn–van Aardenne–Ehrenfest theorem
E239170
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
All labels observed (2)
| Label | Occurrences |
|---|---|
| de Bruijn–van Aardenne–Ehrenfest theorem canonical | 3 |
| de Bruijn–van Aardenne-Ehrenfest–Smith–Tutte theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2169630 — 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–van Aardenne–Ehrenfest theorem Context triple: [N. G. de Bruijn, notableWork, de Bruijn–van Aardenne–Ehrenfest theorem]
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A.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
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B.
Sprague–Grundy theorem
The Sprague–Grundy theorem is a fundamental result in combinatorial game theory that assigns each impartial game position a nonnegative integer (its Grundy value), allowing such games to be analyzed and combined via nim-like addition.
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C.
H-theorem
The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
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D.
Gell-Mann–Low theorem
The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
-
E.
Herbrand's theorem
Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
- 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–van Aardenne–Ehrenfest theorem Target entity description: The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
-
A.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
B.
Sprague–Grundy theorem
The Sprague–Grundy theorem is a fundamental result in combinatorial game theory that assigns each impartial game position a nonnegative integer (its Grundy value), allowing such games to be analyzed and combined via nim-like addition.
-
C.
H-theorem
The H-theorem is Boltzmann’s foundational result in statistical mechanics that explains the irreversible increase of entropy in a gas from time-reversible microscopic dynamics, providing a key link between mechanics and the second law of thermodynamics.
-
D.
Gell-Mann–Low theorem
The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
-
E.
Herbrand's theorem
Herbrand's theorem is a fundamental result in mathematical logic and proof theory that characterizes the validity of first-order formulas via finite sets of ground instances, forming a basis for automated theorem proving.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorics theorem
ⓘ
mathematical theorem ⓘ |
| appliesTo |
Eulerian directed graphs
ⓘ
de Bruijn graphs ⓘ
linked to:
de Bruijn graph
directed graphs ⓘ |
| areaOfApplication |
combinatorial generation
ⓘ
information theory ⓘ network routing ⓘ sequence design ⓘ |
| assumes |
balanced in-degree and out-degree at each vertex
ⓘ
finite directed graph ⓘ graph is strongly connected ⓘ |
| characterizes |
number of Eulerian circuits in a directed graph
ⓘ
number of Eulerian cycles in a de Bruijn graph ⓘ |
| concernsProperty |
Eulerian digraph
ⓘ
in-degree equals out-degree at every vertex ⓘ strongly connected directed graphs ⓘ |
| field |
combinatorics
ⓘ
discrete mathematics ⓘ enumerative combinatorics ⓘ graph theory ⓘ |
| formalizes | enumeration of Eulerian tours in finite directed graphs ⓘ |
| givesFormulaFor | count of Eulerian circuits via arborescences and degree factorials ⓘ |
| historicalPeriod | 20th century mathematics ⓘ |
| implies | existence of Eulerian circuit under degree and connectivity conditions ⓘ |
| mathematicalDiscipline |
combinatorial enumeration
ⓘ
theory of directed graphs ⓘ |
| namedAfter |
Nicolaas Govert de Bruijn
ⓘ
linked to:
N. G. de Bruijn
T. van Aardenne-Ehrenfest ⓘ |
| relatedTo |
BEST theorem
ⓘ
de Bruijn graph ⓘ de Bruijn sequence ⓘ matrix-tree theorem ⓘ |
| supports |
analysis of feedback shift register sequences
ⓘ
construction of de Bruijn sequences of given order ⓘ enumeration of cyclic words with given subword structure ⓘ |
| topic |
Eulerian circuit
ⓘ
linked to:
Eulerian trail
Eulerian trail ⓘ cycle decomposition ⓘ |
| usedIn |
coding theory
ⓘ
combinatorial constructions ⓘ design of de Bruijn sequences ⓘ discrete structures ⓘ graph enumeration ⓘ |
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
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Input
Subject: de Bruijn–van Aardenne–Ehrenfest theorem Description of subject: The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: de Bruijn–van Aardenne–Ehrenfest theorem