We describe a method for computing rank (and determining quasipositivity) in the free group using dynamic programming. The algorithm is adapted to computing upper bounds on the rank for braids. We test our method on a table of knots by identifying quasipositive knots and calculating the ribbon genus. We consider the possibility that rank is not theoretically computable and prove some partial results that would classify its computational complexity. We then present a method for effectively brute force searching band presentations of small rank and conjugate length.
College and Department
Physical and Mathematical Sciences
BYU ScholarsArchive Citation
Meiners, Justin, "Computing the Rank of Braids" (2021). Theses and Dissertations. 8947.
braid group, free group, rank, quasipositive, algorithm, ribbon genus