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A PARTIAL ORDERING OF KNOTS AND LINKS THROUGH DIAGRAMMATIC UNKNOTTING.
- Source :
-
Journal of Knot Theory & Its Ramifications . Apr2009, Vol. 18 Issue 4, p505-522. 18p. 13 Diagrams. - Publication Year :
- 2009
-
Abstract
- In this paper we define a partial ordering of knots and links using a special property derived from their minimal diagrams. A link $\mathcal{K}'$ is called a predecessor of a link $\mathcal{K}$ if $Cr(\mathcal{K}') < Cr(\mathcal{K})$ and a diagram of $\mathcal{K}'$ can be obtained from a minimal diagram D of $\mathcal{K}$ by a single crossing change. In such a case, we say that $\mathcal{K}' < \mathcal{K}$. We investigate the sets of links that can be obtained by single crossing changes over all minimal diagrams of a given link. We show that these sets are specific for different links and permit partial ordering of all links. Some interesting results are presented and many questions are raised. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 18
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 38595633
- Full Text :
- https://doi.org/10.1142/S0218216509007026