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We develop a model characterizing all possible knots and links arising fromrecombination starting with a twist knot substrate, extending previous work ofBuck and Flapan. We show that all knot or link products fall into threewell-understood families of knots and links, and prove that given a positiveinteger $n$, the number of product knots and links with minimal crossing numberequal to $n$ grows proportionally to $n^5$. In the (common) case of twist knotsubstrates whose products have minimal crossing number one more than thesubstrate, we prove that the types of products are tightly prescribed. Finally,we give two simple examples to illustrate how this model can help determinepreviously uncharacterized experimental data.

Characterization of Knots and Links Arising From Site-specific Recombination on Twist Knots