The warping polynomial of a knot diagram

2011/09/27 by Shimizu, Ayaka
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1109.5898

Abstract

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.

Related

• The warping degree of a knot diagram
• Lower bounds for the warping degree of a knot projection
• The warping matrix of a knot diagram
• Prime alternating knots of minimal warping degree two
• A note on the unknotting number and the region unknotting number of weaving knots