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Mosaic number of knots.
- Source :
- Journal of Knot Theory & Its Ramifications; Nov2014, Vol. 23 Issue 13, p-1, 8p
- Publication Year :
- 2014
-
Abstract
- Lomonaco and Kauffman developed knot mosaics to give a definition of a quantum knot system. This definition is intended to represent an actual physical quantum system. A knot n-mosaic is an n × n matrix of 11 kinds of specific mosaic tiles representing a knot or a link. The mosaic number m(K) of a knot K is the smallest integer n for which K is representable as a knot n-mosaic. In this paper, we establish an upper bound on the mosaic number of a knot or a link K in terms of the crossing number c(K). Let K be a nontrivial knot or a non-split link except the Hopf link. Then m(K) ≤ c(K) + 1. Moreover if K is prime and non-alternating except link, then m(K) ≤ c(K) - 1. [ABSTRACT FROM AUTHOR]
- Subjects :
- KNOT theory
NUMBER theory
MATHEMATICAL bounds
HOPF algebras
MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 23
- Issue :
- 13
- Database :
- Complementary Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 100437745
- Full Text :
- https://doi.org/10.1142/S0218216514500692