Involve: A Journal of Mathematics

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

Enumerating spherical $n$-links

Madeleine Burkhart and Joel Foisy

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

combinatorics topological graph theory linking enumeration


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

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Supplemental materials

  • Distinct embeddings for links.