A Transfer Matrix approach to the Enumeration of Knots

Jesper-Lykke Jacobsen (1) , Paul Zinn-Justin (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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.

Mots clés: Mathematical Physics; Combinatorics; Statistical Mechanics

Domaines: Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]

Jesper-Lykke Jacobsen, Paul Zinn-Justin. A Transfer Matrix approach to the Enumeration of Knots. Journal of Knot and its Theoretical Ramifications, 2002, 11, pp.739-758. ⟨hal-00002341⟩