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- Title
ON THE RELATIONSHIP BETWEEN MINIMAL LATTICE KNOTS AND MINIMAL CUBE KNOTS.
- Authors
MANN, CASEY; MCLOUD-MANN, JENNIFER
- Abstract
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.
- Subjects
KNOTS &; splices; ROPEWORK; LATTICE theory; MARLINSPIKE seamanship; KNOT theory; LOW-dimensional topology
- Publication
Journal of Knot Theory & Its Ramifications, 2005, Vol 14, Issue 7, p841
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216505004111