## Involve: A Journal of Mathematics

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

### Enumerating spherical $n$-links

#### 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 $4≤n≤8$.

#### Article information

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

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

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

#### 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

#### 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.
• N. J. A. Sloane, “Number of trees with $n$ unlabeled nodes”, 2006, http://oeis.org/A000055.