Alexander–Briggs notation
E169181
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Alexander–Briggs notation canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T1483784 — 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: Alexander–Briggs notation Context triple: [Conway notation for knots, relatedTo, Alexander–Briggs notation]
-
A.
Conway notation for knots
Conway notation for knots is a mathematical system introduced by John H. Conway that encodes knot and link diagrams into concise symbolic expressions to classify and study them.
-
B.
Whyte notation
Whyte notation is a system for classifying steam locomotives by their wheel arrangement using a sequence of numbers separated by hyphens.
-
C.
Conway groups
Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.
-
D.
Conway chained arrow notation
Conway chained arrow notation is a mathematical system of hyper-operator-style notation introduced by John Horton Conway to concisely represent extremely large numbers.
-
E.
Weyl
Weyl is a surname most famously associated with Hermann Weyl, a prominent 20th-century mathematician and theoretical physicist known for major contributions to group theory, quantum mechanics, and the foundations of mathematics.
- 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: Alexander–Briggs notation Target entity description: 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.
-
A.
Conway notation for knots
Conway notation for knots is a mathematical system introduced by John H. Conway that encodes knot and link diagrams into concise symbolic expressions to classify and study them.
-
B.
Whyte notation
Whyte notation is a system for classifying steam locomotives by their wheel arrangement using a sequence of numbers separated by hyphens.
-
C.
Conway groups
Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.
-
D.
Conway chained arrow notation
Conway chained arrow notation is a mathematical system of hyper-operator-style notation introduced by John Horton Conway to concisely represent extremely large numbers.
-
E.
Weyl
Weyl is a surname most famously associated with Hermann Weyl, a prominent 20th-century mathematician and theoretical physicist known for major contributions to group theory, quantum mechanics, and the foundations of mathematics.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
classification scheme
ⓘ
knot notation system ⓘ |
| appliesTo |
prime knots
ⓘ
tame knots ⓘ |
| assumes | minimal crossing diagrams for knots ⓘ |
| basedOn |
crossing number of a knot
ⓘ
ordering of knots in knot tables ⓘ |
| classificationCriterion |
lexicographic order within same crossing number
ⓘ
minimal crossing number ⓘ |
| classificationType | catalog-style ⓘ |
| defines | unique label for each prime knot up to a given crossing number ⓘ |
| describes | knot by its minimal crossing number and index within that crossing number ⓘ |
| distinctFrom |
Conway notation for knots
ⓘ
Dowker–Thistlethwaite notation ⓘ |
| distinguishes | knots with same crossing number by index ⓘ |
| domain | topology ⓘ |
| example |
3_1 denotes the trefoil knot
ⓘ
4_1 denotes the figure-eight knot ⓘ |
| field | knot theory ⓘ |
| hasProperty |
each label is intended to correspond to a distinct knot type
ⓘ
labels are not invariant under changes in knot tables beyond crossing number and index ⓘ |
| historicalPeriod | early 20th century ⓘ |
| influenced |
Dowker–Thistlethwaite notation
ⓘ
surface form:
Rolfsen knot table notation
modern knot tabulation practices ⓘ |
| introducedBy |
Garrett Birkhoff
ⓘ
surface form:
Garrett Birkhoff Briggs
James Waddel Alexander ⓘ
surface form:
James Waddell Alexander II
|
| introducedInPublication | "On types of knotted curves" ⓘ |
| introducedInYear | 1926 ⓘ |
| language | symbolic notation ⓘ |
| namedAfter |
Garrett Birkhoff
ⓘ
surface form:
Garrett Birkhoff Briggs
James Waddel Alexander ⓘ
surface form:
James Waddell Alexander II
|
| notationFormat |
c_n
ⓘ
c_n^m ⓘ |
| relatedTo |
Hoste–Thistlethwaite–Weeks knot tables
ⓘ
Rolfsen notation ⓘ |
| requires | determination of minimal crossing number for each knot ⓘ |
| scope | knots up to a fixed crossing number in standard tables ⓘ |
| subfield | low-dimensional topology ⓘ |
| supports | systematic enumeration of prime knots ⓘ |
| usedBy |
knot theorists
ⓘ
topologists ⓘ |
| usedFor |
classifying knots
ⓘ
naming knots ⓘ |
| usedIn | knot tables in classical knot theory literature ⓘ |
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: Alexander–Briggs notation Description of subject: 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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.