Vol. 11, No. 2, 2018

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Enumerating spherical $n$-links

Madeleine Burkhart and Joel Foisy

Vol. 11 (2018), No. 2, 195–206

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.

combinatorics, topological graph theory, linking, enumeration
Mathematical Subject Classification 2010
Primary: 05C30
Secondary: 05C10, 57M15
Supplementary material

Distinct embeddings for links

Received: 15 January 2015
Revised: 30 January 2016
Accepted: 5 December 2016
Published: 17 September 2017

Communicated by Jim Hoste
Madeleine Burkhart
Mathematics Department
University of Washington
Seattle, WA
United States
Joel Foisy
Department of Mathematics
SUNY Potsdam
Potsdam, NY
United States