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arXiv · 1205.5256

Stick index of knots and links in the cubic lattice

Colin Adams·Michelle Chu·Thomas Crawford·Stephanie Jensen Kyler Siegel·Liyang Zhang
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Abstract

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.

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Colin Adams, Michelle Chu, Thomas Crawford, Stephanie Jensen Kyler Siegel, Liyang Zhang. 2012-05-23. Stick index of knots and links in the cubic lattice. https://doi.org/10.1142/s0218216511009935

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