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A partial ordering of knots and links through diagrammatic unknotting
Journal of Knot Theory and its Ramifications
In this paper we de. ne a partial ordering of knots and links using a special property derived from their minimal diagrams. A link K' is called a predecessor of a link K if Cr(K') < Cr(K) and a diagram of K' can be obtained from a minimal diagram D of K by a single crossing change. In such a case, we say that K' < 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.
Knots, links, crossing number, unknotting number, UNLINKING NUMBER, 2-BRIDGE KNOTS, CLASSIFICATION
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