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
Knot Theory, Unknotting Problem
Bachelor of Arts
Senior Independent Study Thesis
© Copyright 2017 Dana Foley