Meander diagrams of virtual knots

Abstract

For classical knots, there is a concept of (semi)meander diagrams; in this short note we generalize this concept to virtual knots and prove that the classes of meander and semimeander diagrams are universal (this was known for classical knots). We also introduce a new class of invariants for virtual knots -- virtual $k$-arc crossing numbers and we use Manturov projection to show that for all classical knots the virtual $k$-arc crossing number equals to the classical $k$-arc crossing number.