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- Title
STICK INDEX OF KNOTS AND LINKS IN THE CUBIC LATTICE.
- Authors
ADAMS, COLIN; CHU, MICHELLE; CRAWFORD, THOMAS; JENSEN, STEPHANIE; SIEGEL, KYLER; ZHANG, LIYANG
- 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.
- Subjects
KNOT theory; LATTICE theory; DIMENSIONAL analysis; INVARIANTS (Mathematics); MATHEMATICAL analysis; TORUS; LOW-dimensional topology
- Publication
Journal of Knot Theory & Its Ramifications, 2012, Vol 21, Issue 5, p1250041-1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216511009935