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Planar Diagram

The PD (Planar Diagram) form for a virtual knot diagram is obtained by numbering the edges of the diagram in ascending order, beginning at some point and travelling along the diagram. Virtual crossings are ignored, and after each non-virtual crossing is encountered, the new edge is numbered. Then, at each crossing, list the edges, beginning with the edge incoming on the under strand, and proceeding counter-clockwise. Crossings are indicated like X[i,j,k,l], where i, j, k, and l are the four edges at that crossing.

For example, the PD of virtual knot 2.1, seen below, is X[2,4,3,1], X[3,1,4,2].

See also: Planar Diagrams at Dror Bar-Natan's Knot Atlas.