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.Comment: 20 pages, 11 figures, 14 table
