Arc index of pretzel knots of type $(-p,q,r)$

Details Arc index of pretzel knots of type $(-p,q,r)$ Arc index of pretzel knots of type $(-p,q,r)$

2012-04-03

arxiv.org/abs/1204.0597v1

Mathematics

Geometric Topology

10 pages, 7 figures, 2 tables

Scientific paper

We computed the arc index for the pretzel knots $K=P(-p,q,r)$ with
$p,q,r\ge2$, $r\geq q$ 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 $p\ge3$ and
$q=3$, then $\alpha(K)=c(K)-1$. If $p\ge5$ and $q=4$, then $\alpha(K)=c(K)-2$.

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