Quadruple crossing number of knots and links

Abstract

A quadruple crossing is a crossing in a projection of a knot or link that has four strands of the knot passing straight through it. A quadruple crossing projection is a projection such that all of the crossings are quadruple crossings. In a previous paper, it was proved that every knot and link has a quadruple crossing projection and hence, every knot has a minimal quadruple crossing number. In this paper, we investigate quadruple crossing number, and in particular, use the span of the bracket polynomial to determine quadruple crossing number for a variety of knots and links.

11 pages, 7 figures, correction to one of the skein relations and addition to attributions in introduction

References in corpus (2)

• Knot projections with a single multi-crossing
• Bounds on Übercrossing and Petal Numbers for Knots

Cited by in corpus (5)

• Multi-crossing Number for Knots and the Kauffman Bracket Polynomial
• Virtual Multicrossings and Petal Diagrams for Virtual Knots and Links
• Weak rectangular diagrams, multi-crossing number, and arc index
• Petal grid diagrams of torus knots
• Strict Inequalities for the $n$-crossing Number