Gauss code
E656663
Gauss code is a combinatorial encoding of a knot or plane curve that records the sequence of crossings encountered along the curve.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Gauss code canonical | 1 |
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial encoding
ⓘ
knot invariant ⓘ |
| alternativeTo |
Dowker code
NERFINISHED
ⓘ
planar diagram notation ⓘ |
| appliesTo |
generic immersed closed curves in the plane
ⓘ
knot projections with transverse double points ⓘ |
| basedOn |
traversal of a knot diagram
ⓘ
traversal of a plane curve ⓘ |
| canBeExtendedTo | virtual knot theory ⓘ |
| captures | combinatorial structure of crossings ⓘ |
| constraint | each crossing label appears exactly twice ⓘ |
| describes |
knot
ⓘ
plane curve ⓘ |
| doesNotFullyDetermine | embedding in three-dimensional space ⓘ |
| encodes |
order of crossings along a curve
ⓘ
orientation information of a knot diagram ⓘ over-under information at crossings ⓘ sequence of crossings ⓘ |
| field |
combinatorics
ⓘ
knot theory ⓘ topology ⓘ |
| limitation | not every abstract Gauss code is realizable as a planar knot diagram ⓘ |
| namedAfter | Carl Friedrich Gauss NERFINISHED ⓘ |
| relatedTo |
Dowker–Thistlethwaite code
NERFINISHED
ⓘ
Gauss diagram NERFINISHED ⓘ Reidemeister moves NERFINISHED ⓘ knot diagram ⓘ oriented Gauss code ⓘ planar graph embeddings ⓘ signed Gauss code ⓘ |
| representationForm |
sequence of labels
ⓘ
word over an alphabet of crossing labels ⓘ |
| requires |
choice of orientation of the curve
ⓘ
choice of starting point on the curve ⓘ |
| studiedIn |
knot tabulation
ⓘ
topological graph theory ⓘ |
| usedFor |
algorithmic manipulation of knots
ⓘ
classification of knots ⓘ computer representation of knot diagrams ⓘ reconstruction of knot diagrams up to equivalence ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.