Enumeration of Chord Diagrams without Loops and Parallel Chords
Combinatorics
2017-09-18 v1
Abstract
We enumerate chord diagrams without loops and without both loops and parallel chords. We show that the former ones describe Hamiltonian paths in -dimensional octahedrons. The latter ones are also known as shapes. For labelled diagrams we obtain generating functions, for unlabelled ones we derive recurrence relations.
Keywords
Cite
@article{arxiv.1601.05073,
title = {Enumeration of Chord Diagrams without Loops and Parallel Chords},
author = {Evgeniy Krasko and Alexander Omelchenko},
journal= {arXiv preprint arXiv:1601.05073},
year = {2017}
}
Comments
20 pages, 17 figures, 2 tables