A PARTIAL ORDERING OF KNOTS AND LINKS THROUGH DIAGRAMMATIC UNKNOTTING.

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]