Tool to identify a node and convert it to different notations (Alexander – Briggs – Rolfsen, Dowker – Thistlethwaite, Conway)
Knots Notation - dCode
Tag(s) : Notation System, Symbol Substitution
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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.
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.
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.
Conway's notation was proposed in his theory of entanglements in 1970. This notation describes the node according to its properties.