Involve: A Journal of Mathematics

  • Involve
  • Volume 11, Number 2 (2018), 195-206.

Enumerating spherical $n$-links

Madeleine Burkhart and Joel Foisy

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at msp.org/involve.

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We investigate spherical links: that is, disjoint embeddings of 1-spheres and 0-spheres in the 2-sphere, where the notion of a split link is analogous to the usual concept. In the quest to enumerate distinct nonsplit n-links for arbitrary n, we must consider when it is possible for an embedding of circles and an even number of points to form a nonsplit link. The main result is a set of necessary and sufficient conditions for such an embedding. The final section includes tables of the distinct embeddings that yield nonsplit n-links for 4n8.

Article information

Source
Involve, Volume 11, Number 2 (2018), 195-206.

Dates
Received: 15 January 2015
Revised: 30 January 2016
Accepted: 5 December 2016
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513775056

Digital Object Identifier
doi:10.2140/involve.2018.11.195

Mathematical Reviews number (MathSciNet)
MR3733951

Zentralblatt MATH identifier
06817014

Subjects
Primary: 05C30: Enumeration in graph theory
Secondary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25] 57M15: Relations with graph theory [See also 05Cxx]

Keywords
combinatorics topological graph theory linking enumeration

Citation

Burkhart, Madeleine; Foisy, Joel. Enumerating spherical $n$-links. Involve 11 (2018), no. 2, 195--206. doi:10.2140/involve.2018.11.195. https://projecteuclid.org/euclid.involve/1513775056


Export citation

References

  • D. Archdeacon and F. Sagols, “Nesting points in the sphere”, Discrete Math. 244:1-3 (2002), 5–16.
  • V. Guillemin and A. Pollack, Differential topology, Printice-Hall, Englewood Cliffs, NJ, 1974.
  • F. Harary, Graph theory, Addison-Wesley, Reading, MA, 1969.
  • J. Hoste, “The enumeration and classification of knots and links”, pp. 209–232 in Handbook of knot theory, edited by W. Menasco and M. Thistlethwaite, Elsevier, Amsterdam, 2005.
  • N. J. A. Sloane, “Number of trees with $n$ unlabeled nodes”, 2006, http://oeis.org/A000055.

Supplemental materials

  • Distinct embeddings for links.