Enumerating spherical n-links

Burkhart, Madeleine; Foisy, Joel

doi:10.2140/involve.2018.11.195

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Enumerating spherical $n$-links

Madeleine Burkhart and Joel Foisy

Vol. 11 (2018), No. 2, 195–206

DOI: 10.2140/involve.2018.11.195

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 $4 \leq n \leq 8$ .

Keywords

combinatorics, topological graph theory, linking, enumeration

Mathematical Subject Classification 2010

Primary: 05C30

Secondary: 05C10, 57M15

Supplementary material

Distinct embeddings for links

Milestones

Received: 15 January 2015

Revised: 30 January 2016

Accepted: 5 December 2016

Published: 17 September 2017

Communicated by Jim Hoste

Authors

Madeleine Burkhart
Mathematics Department University of Washington Seattle, WA United States

Joel Foisy
Department of Mathematics SUNY Potsdam Potsdam, NY United States

Vol. 11, No. 2, 2018