A Transfer Matrix approach to the Enumeration of Knots

Jesper-Lykke Jacobsen 1, Paul Zinn-Justin 1

Journal of Knot and its Theoretical Ramifications 11 (2002) 739-758

We propose a new method to enumerate alternating knots using a transfer matrix approach. We apply it to count numerically various objects, including prime alternating tangles with two connected components, up to order 18--22, and comment on the large-order behavior in connection with one of the authors' conjecture.

  • 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE),
    CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot