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Knots Notation

Tool to identify a node and convert it to different notations (Alexander – Briggs – Rolfsen, Dowker – Thistlethwaite, Conway)

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Knots Notation -

Tag(s) : Notation System, Symbol Substitution

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# Knots Notation

## Knots Identifier/Decoder

 Notation Alexander–Briggs–Rolfsen (XY) Dowker–Thistlethwaite (X Y Z) Conway ([XY])

## Answers to Questions (FAQ)

### What is the knot notation? (Definition)

In node theory, in order to distinguish the different types of nodes and to characterize them in a unique way, several notations have been proposed.

### What is the Alexander–Briggs–Rolfsen notation?

The Alexander – Briggs – Rolfsen notation is one of the oldest, presented in 1927, this notation of nodes allows an organization according to the number of crossings.

The notation is presented with 2 numbers, the first is the number of crossings, the second is the order among all the nodes having the same number of crossings (sometimes indicated as a subscript). This second number is arbitrary but tends to represent the complexity of the node, the simpler nodes have small indices.

Example: The trefoil knot is represented 31 ou 31

### What is the Dowker–Thistlethwaite notation?

The Dowker – Thistlethwaite notation is named after Clifford Hugh Dowker and Morwen Thistlethwaite. The notation is generated by traversing the node from any point and any direction, noting each of the n crossings from 1 to 2n in order (the crossings are visited 2 times, so they are noted 2 times) with an additional rule : if the crossing is done from above, note -n instead of n. Then remove all odd numbers from the list obtained. The final Dowker – Thistlethwaite notation is the remaining even number list.

Example: The trefoil knot is represented 4,6,2 (or -4,-6,-2)

### What is the Conway notation?

Conway's notation was proposed in his theory of entanglements in 1970. This notation describes the node according to its properties.

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Knots Notation on dCode.fr [online website], retrieved on 2023-09-27, https://www.dcode.fr/knot-notation

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