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arxiv: 1204.0597 · v3 · pith:INMXZ3GDnew · submitted 2012-04-03 · 🧮 math.GT

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

classification 🧮 math.GT
keywords alphaindexthenknotspretzelcomputedcrossingequals
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We computed the arc index for some of 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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