2021/01/03 by William Qin, Qin, William
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2101.00695
openalex publication_date 2021/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
HOMFLY polynomials are one of the major knot invariants being actively studied. They are difficult to compute in the general case but can be far more easily expressed in certain specific cases. In this paper, we examine two particular knots, as well as one more general infinite class of knots. From our calculations, we see some apparent patterns in the polynomials for the knots 935 and 946, and in particular their F-factors. These properties are of a form that seems conducive to finding a general formula for them, which would yield a general formula for the HOMFLY polynomials of the two knots. Motivated by these observations, we demonstrate and conjecture some properties both of the F-factors and HOMFLY polynomials of these knots and of the more general class that contains them, namely pretzel knots with 3 odd parameters. We make the first steps toward a matrix-less general formula for the HOMFLY polynomials of these knots.