UNKNOTTING NUMBERS OF DIAGRAMS OF A GIVEN NONTRIVIAL KNOT ARE UNBOUNDED-Reference-Cited by-同舟云学术

UNKNOTTING NUMBERS OF DIAGRAMS OF A GIVEN NONTRIVIAL KNOT ARE UNBOUNDED

Published:2009-08 Issue:08 Volume:18 Page:1049-1063
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

TANIYAMA KOUKI¹

Affiliation:

1. Department of Mathematics, School of Education, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan

Abstract

We show that for any nontrivial knot K and any natural number n, there is a diagram D of K such that the unknotting number of D is greater than or equal to n. It is well-known that twice the unknotting number of K is less than or equal to the crossing number of K minus one. We show that the equality holds only when K is a (2, p)-torus knot.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216509007361

Reference12 articles.

1. UNKNOTTING NUMBERS AND MINIMAL KNOT DIAGRAMS

2. A note on unknotting number

3. J. Conway, Computational Problems in Abstract Algebra (Pergamon Press, Oxford, 1967) pp. 329–358.

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