#### 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
##### 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 $4\le n\le 8$.

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