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The warping polynomial of a knot diagram

We introduce the warping polynomial of an oriented knot diagram. In this paper, we characterize the warping polynomial, and define the span of a knot to be the minimal span of the warping polynomial for all diagrams of the knot. We show that the span of a knot is one if and only if it is non-trivial and alternating, and we give an inequality between the span and the dealternating number.

preprint2011arXivOpen access
Ayaka Shimizu
math.GT
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Ayaka Shimizu

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