English

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 nn-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