Stick numbers of -bridge knots and links

Authors:
Youngsik Huh, Sungjong No and Seungsang Oh

Journal:
Proc. Amer. Math. Soc. **139** (2011), 4143-4152

MSC (2010):
Primary 57M25, 57M27

Published electronically:
March 16, 2011

MathSciNet review:
2823059

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Abstract | References | Similar Articles | Additional Information

Abstract: Negami found an upper bound on the stick number of a nontrivial knot in terms of the minimal crossing number of the knot, which is . Furthermore, McCabe proved that for a -bridge knot or link, except in the cases of the unlink and the Hopf link. In this paper we construct any -bridge knot or link of at least six crossings by using only straight sticks. This gives a new upper bound on stick numbers of -bridge knots and links in terms of crossing numbers.

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Additional Information

**Youngsik Huh**

Affiliation:
Department of Mathematics, School of Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea

Email:
yshuh@hanyang.ac.kr

**Sungjong No**

Affiliation:
Department of Mathematics, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul 136-701, Republic of Korea

Email:
blueface@korea.ac.kr

**Seungsang Oh**

Affiliation:
Department of Mathematics, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul 136-701, Republic of Korea

Email:
seungsang@korea.ac.kr

DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-10832-3

Keywords:
Knot,
stick number,
2-bridge

Received by editor(s):
March 9, 2010

Received by editor(s) in revised form:
July 22, 2010, and September 16, 2010

Published electronically:
March 16, 2011

Additional Notes:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (No. 2009-0074101).

Communicated by:
Daniel Ruberman

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.