Stick index of knots and links in the cubic lattice

  • Colin Adams
  • , Michelle Chu
  • , Thomas Crawford
  • , Stephanie Jensen
  • , Kyler Siegel
  • , Liyang Zhang

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

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 languageEnglish (US)
Article number1250041
JournalJournal of Knot Theory and its Ramifications
Volume21
Issue number5
DOIs
StatePublished - May 2012
Externally publishedYes

Keywords

  • Lattice stick number
  • composite knots
  • satellite knots
  • torus knots

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