$Classification of $k$-tangle projections using cascade representation$

Classification of $k$-tangle projections using cascade representation

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...

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Veröffentlicht in:	arXiv.org 2010-07
Hauptverfasser:	Bogdanov, Andrey, Meshkov, Vadim, Omelchenko, Alexander, Petrov, Michael
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Enumeration Pictures Representations
Online-Zugang:	Volltext
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Zusammenfassung:	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.
ISSN:	2331-8422

Zusammenfassung:	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.
ISSN:	2331-8422

Classification of \(k\)-tangle projections using cascade representation