Dowker–Thistlethwaite notation

E169182

encoding scheme knot notation mathematical notation

Dowker–Thistlethwaite notation is a numerical encoding system used in knot theory to uniquely represent knot diagrams and facilitate their classification and study.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (6)

Label	Occurrences
Dowker–Thistlethwaite notation canonical	7
Dowker code	2
Dowker–Thistlethwaite code	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	oriented Dowker–Thistlethwaite notation ⓘ linked to: Dowker–Thistlethwaite notation signed Dowker–Thistlethwaite notation ⓘ linked to: 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 ⓘ linked to: Conway notation for knots 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