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Knot fertility and lineage

Jason Cantarella

Department of Mathematics, Boyd Graduate Studies Research Center, University of Georgia, Athens, GA 30602, USA

E-mail Address: jason.cantarella@gmail.com

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Allison Henrich

http://orcid.org/0000-0002-0417-0053

Mathematics Department, Seattle University, 901 12th Ave., Seattle, WA 98122, USA

E-mail Address: henricha@seattleu.edu

Corresponding author.

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Elsa Magness

Mathematics Department, Seattle University, 901 12th Ave., Seattle, WA 98122, USA

E-mail Address: magnesse@seattleu.edu

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Oliver O’Keefe

Mathematics Department, University of St. Thomas, Minnesota, 2115 Summit Avenue, St. Paul, Minnesota 55105, USA

E-mail Address: okeeoo55@stthomas.edu

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Kayla Perez

The Evergreen State College, 2700 Evergreen Parkway NW, Olympia, Washington 98505, USA

E-mail Address: kayla.aperez@yahoo.com

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Eric Rawdon

Mathematics Department, University of St. Thomas, Minnesota, 2115 Summit Avenue, St. Paul, Minnesota 55105, USA

E-mail Address: ejrawdon@stthomas.edu

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, and

Briana Zimmer

University of Washington, Seattle, WA 98185, USA

E-mail Address: brianazimmer@comcast.net

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https://doi.org/10.1142/S0218216517500936Cited by:10 (Source: Crossref)

Abstract

In this paper, we introduce a new type of relation between knots called the descendant relation. One knot $H$ is a descendant of another knot $K$ if $H$ can be obtained from a minimal crossing diagram of $K$ by some number of crossing changes. We explore properties of the descendant relation and study how certain knots are related, paying particular attention to those knots, called fertile knots, that have a large number of descendants. Furthermore, we provide computational data related to various notions of knot fertility and propose several open questions for future exploration.

Keywords:

AMSC: 57M25, 57M27

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