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arxiv: 1411.1850 · v1 · pith:QQVZX5H6new · submitted 2014-11-07 · 🧮 math.GT

Stick numbers of 2-bridge knots and links

classification 🧮 math.GT
keywords bridgeknotlinknumbersstickboundcrossingknots
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Negami found an upper bound on the stick number $s(K)$ of a nontrivial knot $K$ in terms of the minimal crossing number $c(K)$ of the knot which is $s(K) \leq 2 c(K)$. Furthermore McCabe proved $s(K) \leq c(K) + 3$ for a $2$-bridge knot or link, except in the case of the unlink and the Hopf link. In this paper we construct any $2$-bridge knot or link $K$ of at least six crossings by using only $c(K)+2$ straight sticks. This gives a new upper bound on stick numbers of $2$-bridge knots and links in terms of crossing numbers.

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