Unknotting and maximum unknotting numbers-Reference-Cited by-同舟云学术

Unknotting and maximum unknotting numbers

Published:2016-08 Issue:09 Volume:25 Page:1641010
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Zeković Ana¹,Jablan Slavik¹,Kauffman Louis²,Sazdanovic Radmila³,Stošić Marko⁴⁵

Affiliation:

1. Department of Mathematical Sciences, Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11120 Belgrade, Serbia

2. Department of Mathematics, University of Illinois at Chicago, Statistics and Computer Science (m/c 249), 851 South Morgan Street, Chicago, Illinois 60607-7045, USA

3. Department of Mathematics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27695-8205, USA

4. The Mathematical Institute, Knez Mihailova 36, P.O. Box 367, 11001 Belgrade, Serbia

5. CAMGSD, Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal

Abstract

We introduce concepts of the maximum unknotting number and the mixed unknotting number, taking into consideration the Bernhard–Jablan Conjecture about computing the unknotting number based only on minimal knot diagrams. The existence of Kauffman knots (alternating knots, such that a crossing change does not change their minimal crossing number) was first suggested by Kauffman. We extend the concept and offer three related classes of knots named: Kauffman knots, Zeković knots and Taniyama knots.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216516410108

Reference29 articles.

1. H(2)-unknotting operation related to 2-bridge links

2. On Khovanov’s categorification of the Jones polynomial

3. UNKNOTTING NUMBERS AND MINIMAL KNOT DIAGRAMS

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