Knot fertility and lineage
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.
Journal of Knot Theory and Its Ramifications