2018/04/21 by Mustafa Hajij, Hajij, Mustafa, Jesse Levitt +1 · 1 citation
Mathematics · #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #G.4 #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #I.1.2 #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1804.07910
openalex publication_date 2018/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The colored Jones polynomial is a knot invariant that plays a central role in low dimensional topology. We give a simple and an efficient algorithm to compute the colored Jones polynomial of any knot. Our algorithm utilizes the walks along a braid model of the colored Jones polynomial that was refined by Armond from the work of Huynh and Lê. The walk model gives rise to ordered words in a q-Weyl algebra which we address and study from multiple perspectives. We provide a highly optimized Mathematica implementation that exploits the modern features of the software. We include a performance analysis for the running time of our algorithm. Our implementation of the algorithm shows that our method usually runs in faster time than the existing state-of the-art method by an order of magnitude.