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Upper bound on lattice stick number of knots

Published online by Cambridge University Press:  25 April 2013

KYUNGPYO HONG ,
SUNGJONG NO  and
SEUNGSANG OH
KYUNGPYO HONG
Affiliation:
Department of Mathematics, Korea University, Seoul 136-701, Korea. e-mails: cguyhbjm@korea.ac.kr, blueface@korea.ac.kr, seungsang@korea.ac.kr
SUNGJONG NO
Affiliation:
Department of Mathematics, Korea University, Seoul 136-701, Korea. e-mails: cguyhbjm@korea.ac.kr, blueface@korea.ac.kr, seungsang@korea.ac.kr
SEUNGSANG OH
Affiliation:
Department of Mathematics, Korea University, Seoul 136-701, Korea. e-mails: cguyhbjm@korea.ac.kr, blueface@korea.ac.kr, seungsang@korea.ac.kr
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Abstract

The lattice stick number sL(K) of a knot K is defined to be the minimal number of straight line segments required to construct a stick presentation of K in the cubic lattice. In this paper, we find an upper bound on the lattice stick number of a nontrivial knot K, except the trefoil knot, in terms of the minimal crossing number c(K) which is sL(K) ≤ 3c(K) + 2. Moreover if K is a non-alternating prime knot, then sL(K) ≤ 3c(K) − 4.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 1 , July 2013 , pp. 173 - 179
Copyright
Copyright © Cambridge Philosophical Society 2013 

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