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Enumerating
spherical $n$-links
Madeleine Burkhart and Joel Foisy
Vol. 11 (2018), No. 2, 195–206
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Abstract |
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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 -links for arbitrary , 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 -links for . |
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Keywords
combinatorics, topological graph theory, linking,
enumeration
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Mathematical Subject Classification 2010
Primary: 05C30
Secondary: 05C10, 57M15
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Supplementary material |
Milestones
Received: 15 January 2015
Revised: 30 January 2016
Accepted: 5 December 2016
Published: 17 September 2017
Communicated by Jim Hoste
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Authors |
| Madeleine Burkhart | |
| Mathematics Department University of Washington Seattle, WA United States |
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| Joel Foisy | |
| Department of Mathematics SUNY Potsdam Potsdam, NY United States |
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