The warping polynomial of a knot diagram

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.

21 pages, 18 figures

References in corpus (1)

• Minimal generating sets of Reidemeister moves

Cited by in corpus (1)

• Quantization of the crossing number of a knot diagram