[email protected] joe-starr.com Joecstarr joseph-c-starr
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.