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Stick index of knots and links in the cubic lattice

The cubic lattice stick index of a knot type is the least number of sticks necessary to construct the knot type in the 3-dimensional cubic lattice. We present the cubic lattice stick index of various knots and links, including all (p,p+1)-torus knots, and show how composing and taking satellites can be used to obtain the cubic lattice stick index for a relatively large infinite class of knots. Additionally, we present several bounds relating cubic lattice stick index to other known invariants.

preprint2012arXivOpen access
Colin AdamsMichelle ChuThomas CrawfordStephanie Jensen Kyler SiegelLiyang Zhang
math.GT
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Open access5 authors1 topic
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Colin AdamsMichelle ChuThomas CrawfordStephanie Jensen Kyler SiegelLiyang Zhang

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