Doctor of Philosophy in Mathematics
University of Iowa
In my thesis titled The Tanglenomicon: Tabulation of Arborescent Tangles, I
enumerated a class of knot-theoretic objects called arborescent tangles. I identified a unique
(up to isotopy) representative for each arborescent tangle, the Right Leaning Identity Tangle
Tree (RLITT). I then created and proved correct the abstract algorithms needed for enumeration of
RLITT. Furthermore, I designed a process architecture that connects mathematical research with
software design, including formal design and validation activities. Within that process I
developed a modular software architecture in C for general computational knot theoretic use
cases. Using this architecture, I implemented my theoretical algorithms and tabulated arborescent
tangles up to 18 crossings.