Classification of $k$-tangle projections using cascade representation

Andrey Bogdanov; Vadim Meshkov; Alexander Omelchenko; Michael Petrov

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arXiv · 0712.3859

Classification of $k$-tangle projections using cascade representation

Andrey Bogdanov·Vadim Meshkov·Alexander Omelchenko·Michael Petrov

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Abstract

The paper addresses the $k$-tangle enumeration problem. We introduce a notion of cascade diagram for $k$-tangle projections. An effective enumeration algorithm for projections is proposed based on cascade representation. Tangles projections with up to 12 crossings are tabulated. We provide also pictures of alternating $k$-tangles with 5 crossing or less.

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Andrey Bogdanov, Vadim Meshkov, Alexander Omelchenko, Michael Petrov. 2010-07-18. Classification of $k$-tangle projections using cascade representation. https://arxiv.org/abs/0712.3859

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