Arc index of pretzel knots of type $(-p, q, r)$
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- by Hwa Jeong Lee and Gyo Taek Jin HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 1 (2014), 135-147
Abstract:
We computed the arc index for some of the pretzel knots $K=P(-p,q,r)$ with $p,q,r\ge 2$, $r\geq q$ and at most one of $p,q,r$ is even. If $q=2$, then the arc index $\alpha (K)$ equals the minimal crossing number $c(K)$. If $p\ge 3$ and $q=3$, then $\alpha (K)=c(K)-1$. If $p\ge 5$ and $q=4$, then $\alpha (K)=c(K)-2$.References
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Additional Information
- Hwa Jeong Lee
- Affiliation: Department of Mathematics, Chung-Ang University, 221 Heukseok-dong, Dongjak-gu, Seoul 156-756, Korea
- Address at time of publication: Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Korea
- MR Author ID: 988416
- Email: hjwith@cau.ac.kr, hjwith@kaist.ac.kr
- Gyo Taek Jin
- Affiliation: Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Korea
- MR Author ID: 267226
- Email: trefoil@kaist.ac.kr
- Received by editor(s): April 3, 2012
- Received by editor(s) in revised form: September 12, 2012, August 24, 2013, and December 20, 2013
- Published electronically: December 5, 2014
- Additional Notes: The first author was supported in part by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2010-0024630)
The second author was supported in part by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2011-0027989) - Communicated by: Daniel Ruberman
- © Copyright 2014 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 1 (2014), 135-147
- MSC (2010): Primary 57M27; Secondary 57M25
- DOI: https://doi.org/10.1090/S2330-1511-2014-00015-8
- MathSciNet review: 3284701