1. Knot fertility and lineage.
- Author
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Cantarella, Jason, Henrich, Allison, Magness, Elsa, O'Keefe, Oliver, Perez, Kayla, Rawdon, Eric, and Zimmer, Briana
- Subjects
- *
CHARTS, diagrams, etc. , *MATHEMATICS , *INTEGERS , *POLYNOMIALS , *KNOT theory - Abstract
In this paper, we introduce a new type of relation between knots called the descendant relation. One knot is a descendant of another knot if can be obtained from a minimal crossing diagram of 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. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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