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Article

Enumerating the k-tangle Projections

Journal of Knot Theory and Its Ramifications. 2012. Vol. 21. No. 7. P. 1-17.
A.V.Omelchenko, Bogdanov A., Meshkov V., Petrov M.

The paper addresses the enumeration problem for k-tangles. We introduce the notion of a cascade diagram of a k-tangle projection and suggest an effective enumeration algorithm for projections based on the cascade representation. Tangle projections and alternating tangles with up to 12 crossings are tabulated. We also provide pictures of alternating k-tangles with at most five crossings.