ON THE RELATIONSHIP BETWEEN MINIMAL LATTICE KNOTS AND MINIMAL CUBE KNOTS.
- Resource Type
- Article
- Authors
- MANN, CASEY; MCLOUD-MANN, JENNIFER
- Source
- Journal of Knot Theory & Its Ramifications. Nov2005, Vol. 14 Issue 7, p841-851. 11p. 11 Diagrams.
- Subject
- *KNOTS & splices
*ROPEWORK
*LATTICE theory
*MARLINSPIKE seamanship
*KNOT theory
*LOW-dimensional topology
- Language
- ISSN
- 0218-2165
Lattice knots have been studied in recent years, especially in ℤ3 and with respect to how many edges are required to form a knot. Knots formed from cubes have also been investigated for their ability to tessellate space. In this article, we demonstrate that there is a relationship between the minimum number of edges required to form a lattice knot and the minimum number of cubes required to form the same kind of knot. We further investigate the relationship in the face-centered cubic lattice. [ABSTRACT FROM AUTHOR]