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ENUMERATING THE k-TANGLE PROJECTIONS

Department of Mathematics and Informational Technologies, Saint Petersburg Academic University, Khlopin str. 8/3, Saint Petersburg, Russia

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VADIM MESHKOV

Department of Mathematics and Informational Technologies, Saint Petersburg Academic University, Khlopin str. 8/3, Saint Petersburg, Russia

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ALEXANDER OMELCHENKO

Department of Mathematics and Informational Technologies, Saint Petersburg Academic University, Khlopin str. 8/3, Saint Petersburg, Russia

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, and

MIKHAIL PETROV

Department of Mathematics and Informational Technologies, Saint Petersburg Academic University, Khlopin str. 8/3, Saint Petersburg, Russia

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https://doi.org/10.1142/S0218216512500691Cited by:3 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 57M25, 05C30

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