In mathematics, a knot is a single strand crossed over itself any number of times, and connected at the ends. The Reidemeister Moves have been proven to be the three core moves necessary to fully untangle a knot. We define a set of generalized moves based on the Reidemeister Moves which only reduce or maintain the complexity of a diagram. We provide a proof that these moves are sufficient for untangling all knots, including hard unknots. Additionally, we construct a computer program which reads the projection of a knot in its Extended Gauss Code notation and uses our moves to untangle it to the smallest possible number of crossings.
Computer Science; Mathematics
Foley, Dana, "Monotonic Untangling to Solve the Unknotting Problem" (2017). Senior Independent Study Theses. Paper 7498.
Geometry and Topology
Bachelor of Arts
Senior Independent Study Thesis
© Copyright 2017 Dana Foley