Enumeration of Chord Diagrams without Loops and Parallel Chords

Evgeniy Krasko, Alexander Omelchenko

Abstract


We enumerate chord diagrams without loops and without both loops and parallel chords. For labelled diagrams we obtain generating functions, for unlabelled ones we derive recurrence relations.

Keywords


Chord diagrams; Hamiltonian paths; $n$-Dimensional octahedron; Shapes; Unlabelled enumeration; Generating functions

Full Text: PDF