Title
Knot fertility and lineage
Department/School
Mathematics
Date
11-16-2017
Document Type
Article
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 �� Hcan 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.
Volume
26
Issue
13
Published in
Journal of Knot Theory and Its Ramifications
COinS
Citation/Other Information
Cantarella, J., Henrich, A., Magness, E., O'Keefe, O., Perez, K., Rawdon, E., & Zimmer, B. (2017). Knot fertility and lineage. Journal of Knot Theory and its Ramifications, 26(13) doi:10.1142/S0218216517500936