Virtual Multicrossings and Petal Diagrams for Virtual Knots and Links

TL;DR

This paper extends the concept of multicrossings to virtual knots and links, demonstrating that petal diagrams can be constructed for all virtual knots, thereby broadening the understanding of virtual knot representations.

Contribution

It introduces the extension of multicrossings to virtual knots and proves the universal existence of petal diagrams for all virtual knots.

Findings

Petal diagrams exist for all virtual knots.

Multicrossings are generalized to virtual knots.

Enhanced understanding of virtual knot representations.

Abstract

Multicrossings, which have previously been defined for classical knots and links, are extended to virtual knots and links. In particular, petal diagrams are shown to exist for all virtual knots.