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
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
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.
dCode retains ownership of the "Knots Notation" source code. Except explicit open source licence (indicated Creative Commons / free), the "Knots Notation" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Knots Notation" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Knots Notation" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.
The copy-paste of the page "Knots Notation" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Knots Notation on dCode.fr [online website], retrieved on 2024-11-21,