Hoste–Thistlethwaite–Weeks knot tables
E656662
The Hoste–Thistlethwaite–Weeks knot tables are comprehensive, systematically generated lists of prime knots (and links) organized by crossing number, widely used as a modern extension and refinement of classical knot tabulations in knot theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Hoste–Thistlethwaite–Weeks knot tables canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T7338148 — 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: Hoste–Thistlethwaite–Weeks knot tables Context triple: [Alexander–Briggs notation, relatedTo, Hoste–Thistlethwaite–Weeks knot tables]
-
A.
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite notation is a numerical encoding system used in knot theory to uniquely represent knot diagrams and facilitate their classification and study.
-
B.
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.
-
C.
Wirtinger presentation of knot groups
The Wirtinger presentation of knot groups is a classical method in knot theory that describes the fundamental group of a knot complement using generators and relations derived from a knot diagram.
-
D.
Jones polynomial
The Jones polynomial is a powerful knot invariant in topology that assigns to each knot or link a Laurent polynomial, enabling the distinction of many knots that are indistinguishable by classical invariants.
-
E.
Conway skein triple (L₊, L₋, L₀)
The Conway skein triple (L₊, L₋, L₀) is a standard configuration of three related link diagrams used in knot theory to express how a link invariant, such as the Conway polynomial, changes under local crossing modifications.
- 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: Hoste–Thistlethwaite–Weeks knot tables Target entity description: The Hoste–Thistlethwaite–Weeks knot tables are comprehensive, systematically generated lists of prime knots (and links) organized by crossing number, widely used as a modern extension and refinement of classical knot tabulations in knot theory.
-
A.
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite notation is a numerical encoding system used in knot theory to uniquely represent knot diagrams and facilitate their classification and study.
-
B.
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.
-
C.
Wirtinger presentation of knot groups
The Wirtinger presentation of knot groups is a classical method in knot theory that describes the fundamental group of a knot complement using generators and relations derived from a knot diagram.
-
D.
Jones polynomial
The Jones polynomial is a powerful knot invariant in topology that assigns to each knot or link a Laurent polynomial, enabling the distinction of many knots that are indistinguishable by classical invariants.
-
E.
Conway skein triple (L₊, L₋, L₀)
The Conway skein triple (L₊, L₋, L₀) is a standard configuration of three related link diagrams used in knot theory to express how a link invariant, such as the Conway polynomial, changes under local crossing modifications.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
knot table
ⓘ
mathematical database ⓘ reference work in knot theory ⓘ |
| appliesTo |
links with multiple components
ⓘ
oriented knots ⓘ unoriented knots ⓘ |
| basedOn | systematic computer enumeration ⓘ |
| creator |
Jeff Weeks
ⓘ
Jim Hoste ⓘ Morwen Thistlethwaite ⓘ |
| extends |
Alexander–Briggs knot tables
ⓘ
Tait knot tables ⓘ
linked to:
Alexander–Briggs knot tables
|
| field | knot theory ⓘ |
| hasFeature |
canonical numbering within each crossing number
ⓘ
compatibility with standard knot notations ⓘ data suitable for computer processing ⓘ diagrams for each knot type ⓘ |
| includes |
prime knots up to at least 16 crossings
ⓘ
prime links up to at least 10 crossings ⓘ |
| influenced |
computational approaches in knot theory
ⓘ
modern electronic knot tables ⓘ |
| language | English ⓘ |
| organizedBy | crossing number ⓘ |
| property |
comprehensive for small crossing numbers
ⓘ
computer-assisted ⓘ organized by minimal crossing number ⓘ systematically generated ⓘ |
| relatedTo |
Knot Atlas
ⓘ
Rolfsen knot table ⓘ |
| subject |
links
ⓘ
prime knots ⓘ |
| use |
classification of knots
ⓘ
classification of links ⓘ comparison of knot invariants ⓘ computation of knot invariants ⓘ extension of classical knot tabulations ⓘ testing conjectures in knot theory ⓘ |
| usedBy |
knot theorists
ⓘ
low-dimensional topologists ⓘ mathematical physicists ⓘ |
| usedFor |
benchmarking knot recognition algorithms
ⓘ
building electronic knot databases ⓘ studying distribution of knot invariants ⓘ studying growth of number of knots with crossing number ⓘ |
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: Hoste–Thistlethwaite–Weeks knot tables Description of subject: The Hoste–Thistlethwaite–Weeks knot tables are comprehensive, systematically generated lists of prime knots (and links) organized by crossing number, widely used as a modern extension and refinement of classical knot tabulations in knot theory.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.