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

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

COinS