IN THIS PAPERI construct a state model for the (original) Jones polynomial [5]. (In [6] a state model was constructed for the Conway polynomial.) As we shall see, this model for the Jones polynomialâ€¦ (More)

This paper explores the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of theYangâ€“Baxter equation is a universalâ€¦ (More)

This paper introduces a generalization of the Tutte polynomial [14] that is defined for signed graphs. A signed graph is a graph whose edges are each labelled with a sign (+l or 1). The generalizedâ€¦ (More)

By associating a collection of knots and links to a graph in threedimensional space, we obtain computable invariants of the embedding type of the graph. Two types of isotopy are considered:â€¦ (More)

In this paper, we give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This definition can be viewed as a blueprint for the construction ofâ€¦ (More)

Kuperberg [15] has shown that a virtual knot diagram corresponds (up to generalized Reidemeister moves) to a unique embedding in a thickened surface of minimal genus. If a virtual knot diagram isâ€¦ (More)