Abstract
The cubic lattice stick index of a knot type is the least number of sticks glued end-to-end that are 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.
| Original language | English (US) |
|---|---|
| Article number | 1250041 |
| Journal | Journal of Knot Theory and its Ramifications |
| Volume | 21 |
| Issue number | 5 |
| DOIs | |
| State | Published - May 2012 |
| Externally published | Yes |
Keywords
- Lattice stick number
- composite knots
- satellite knots
- torus knots