Dowker–Thistlethwaite notation
E169182
Dowker–Thistlethwaite notation is a numerical encoding system used in knot theory to uniquely represent knot diagrams and facilitate their classification and study.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Dowker–Thistlethwaite notation canonical | 2 |
| Rolfsen knot table notation | 1 |
| oriented Dowker–Thistlethwaite notation | 1 |
| signed Dowker–Thistlethwaite notation | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1483785 — 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: Dowker–Thistlethwaite notation Context triple: [Conway notation for knots, relatedTo, Dowker–Thistlethwaite 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.
Conway polynomial
The Conway polynomial is an invariant of knots and links in topology that assigns a polynomial to each knot, capturing essential information about its structure and helping distinguish non-equivalent knots.
-
C.
Conway sphere
The Conway sphere is a mathematical construct in knot theory used to decompose knots and links into simpler tangles, named after mathematician John Horton Conway.
-
D.
Whyte notation
Whyte notation is a system for classifying steam locomotives by their wheel arrangement using a sequence of numbers separated by hyphens.
-
E.
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.
- 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: Dowker–Thistlethwaite notation Target entity description: Dowker–Thistlethwaite notation is a numerical encoding system used in knot theory to uniquely represent knot diagrams and facilitate their classification and study.
-
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.
Conway polynomial
The Conway polynomial is an invariant of knots and links in topology that assigns a polynomial to each knot, capturing essential information about its structure and helping distinguish non-equivalent knots.
-
C.
Conway sphere
The Conway sphere is a mathematical construct in knot theory used to decompose knots and links into simpler tangles, named after mathematician John Horton Conway.
-
D.
Whyte notation
Whyte notation is a system for classifying steam locomotives by their wheel arrangement using a sequence of numbers separated by hyphens.
-
E.
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.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
encoding scheme
ⓘ
knot notation ⓘ mathematical notation ⓘ |
| appliesTo |
composite knots
ⓘ
links with modifications ⓘ prime knots ⓘ |
| assumes | knot diagrams are 4‑regular planar graphs ⓘ |
| basedOn | numbering of crossings in a knot diagram ⓘ |
| captures | crossing information of a knot diagram ⓘ |
| distinguishes | mirror images of knots with sign information ⓘ |
| enables |
algorithmic comparison of knots
ⓘ
storage of knot data in databases ⓘ systematic enumeration of prime knots ⓘ |
| encodingType | numerical code ⓘ |
| field | knot theory ⓘ |
| goal | unique representation of knot diagrams up to isotopy ⓘ |
| hasVariant |
Dowker–Thistlethwaite notation
self-linksurface differs
ⓘ
surface form:
oriented Dowker–Thistlethwaite notation
Dowker–Thistlethwaite notation self-linksurface differs ⓘ
surface form:
signed Dowker–Thistlethwaite notation
|
| historicalUse | construction of early comprehensive knot tables ⓘ |
| influenced | later computational encodings of knots ⓘ |
| isInputTo |
algorithms for computing knot invariants
ⓘ
programs for drawing knot diagrams ⓘ |
| limitation |
depends on a chosen direction of traversal
ⓘ
depends on a chosen orientation of the knot diagram ⓘ depends on a chosen starting point on the knot ⓘ |
| mathematicalDomain | topology ⓘ |
| namedAfter |
Clifford Hugh Dowker
ⓘ
Morwen Thistlethwaite ⓘ |
| property |
can distinguish many non‑equivalent knots
ⓘ
each crossing in a knot diagram is assigned a unique even–odd pair ⓘ encodes each crossing by a pair of integers ⓘ even integers correspond to undercrossings or overcrossings depending on convention ⓘ odd integers correspond to the first visit to a crossing in a traversal ⓘ |
| relatedTo |
Alexander–Briggs notation
ⓘ
Conway notation for knots ⓘ
surface form:
Conway notation
Gauss code ⓘ |
| represents | knot diagrams as sequences of integers ⓘ |
| requires |
planar projection of a knot
ⓘ
regular knot diagram with finitely many crossings ⓘ |
| subdomain | low‑dimensional topology ⓘ |
| usedFor |
classification of knots
ⓘ
computer representation of knots ⓘ encoding knot diagrams ⓘ tabulation of knots ⓘ |
| usedIn |
Hoste–Thistlethwaite–Weeks knot tables
ⓘ
computational knot theory ⓘ knot tables ⓘ |
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: Dowker–Thistlethwaite notation Description of subject: Dowker–Thistlethwaite notation is a numerical encoding system used in knot theory to uniquely represent knot diagrams and facilitate their classification and study.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Rolfsen knot table notation
Dowker–Thistlethwaite notation
→
hasVariant
→
Dowker–Thistlethwaite notation
self-linksurface differs
ⓘ
this entity surface form:
signed Dowker–Thistlethwaite notation
Dowker–Thistlethwaite notation
→
hasVariant
→
Dowker–Thistlethwaite notation
self-linksurface differs
ⓘ
this entity surface form:
oriented Dowker–Thistlethwaite notation