Publications

The classification of knots, links, and tangles has applications to fields including molecular biology where proteins are modeled by tangle equations. Online databases contain millions of knots and links including diagrams, notations, and properties. Tangles have not been classified to the same extent despite their close relation to knots and links and usefulness in applications. To build a database of 2-string tangles, we use a Conway-like notation to count and generate tangles using known canonical forms for rational, Montesinos, and generalized Montesinos tangles as building blocks.

Classifying knots, links, and tangles is an ongoing process with applications to fields including molecular biology where protein actions may be modelled by tangle equations. For knots and links, there are databases which list thousands of these shapes including diagrams, notations, and properties. Tangles have not been published to the same level so, while properties can be found for a simple category of tangles (rational tangles), information is still needed for the more complex tangles. To help build a database of 2-string tangles, we use a matrix-like notation to describe any tangle which is more easily interpreted and manipulated by a computer then translated into a more descriptive and common notation (Conway notation).