Conway notation for knots

E29417
classification system encoding scheme knot invariant mathematical notation

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.

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Observed surface forms (1)

Surface form Occurrences
Conway notation 1

Statements (46)

Predicate Object
instanceOf classification system ⓘ
encoding scheme ⓘ
knot invariant ⓘ
mathematical notation ⓘ
appliesTo knots ⓘ
links ⓘ
basedOn tangle decomposition ⓘ
characteristic captures the arrangement of tangles in a knot diagram ⓘ
encodes knot diagrams as strings of numbers ⓘ
often more concise than Dowker–Thistlethwaite notation ⓘ
uses integers and symbols to encode structure ⓘ
creator John H. Conway ⓘ
surface form: John Horton Conway
describedIn John H. Conway's work on enumeration of knots and links ⓘ
field geometric topology ⓘ
knot theory ⓘ
topology ⓘ
hasAdvantage compact representation of complex diagrams ⓘ
facilitates recognition of related knot types ⓘ
provides a systematic way to generate families of knots ⓘ
influenced later computational approaches to knot classification ⓘ
introducedInContextOf study of algebraic knots and links ⓘ
namedAfter John H. Conway ⓘ
surface form: John Horton Conway
notationExample "3 1" for a specific 2-tangle composition ⓘ
"3" for the trefoil knot ⓘ
"4" for the figure-eight knot ⓘ
purpose classification of knots ⓘ
classification of links ⓘ
encoding knot diagrams ⓘ
encoding link diagrams ⓘ
study of knot properties ⓘ
relatedTo Alexander–Briggs notation ⓘ
Conway polynomial ⓘ
Dowker–Thistlethwaite notation ⓘ
rational tangle calculus ⓘ
represents alternating knots ⓘ
composite knots ⓘ
many non-alternating knots ⓘ
prime knots ⓘ
usedIn computer classification of knots ⓘ
knot tables ⓘ
knot tabulation ⓘ
study of alternating link diagrams ⓘ
usesConcept Conway sphere ⓘ
surface form: Conway spheres

algebraic tangles ⓘ
arborescent knots ⓘ
rational tangles ⓘ

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

John → hasConcept → Conway notation for knots ⓘ
subject surface form: John H. Conway
this entity surface form: Conway notation
John H. Conway → notableWork → Conway notation for knots ⓘ
John → notableWork → Conway notation for knots ⓘ
subject surface form: John H. Conway
Horton → notableWork → Conway notation for knots ⓘ
subject surface form: John Horton Conway