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Abstract: The paper addresses the $k$-tangle enumeration problem. We introduce a notionof cascade diagram for $k$-tangle projections. An effective enumerationalgorithm for projections is proposed based on cascade representation. Tanglesprojections with up to 12 crossings are tabulated. We provide also pictures ofalternating $k$-tangles with 5 crossing or less.



Author: Andrey Bogdanov, Vadim Meshkov, Alexander Omelchenko, Michael Petrov

Source: https://arxiv.org/



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