We collect statistics which consist of the coefficients in the expansion of the generating polynomials that count the Kauffman states associated with certain classes of pretzel knots having n tangles, of r half-twists respectively.

We construct an integer polynomial whose coefficients enumerate the Kauffman states of the two-bridge knot with Conway's notation C(n, r).

The present paper is concerned with the enumeration of the state diagrams for some classes of knot shadows endowed with the usual connected sum operation. We focus on shadows that are recursively generated by knot shadows with up to 3 crossings, and for which the enumeration problem is solved with the help of generating polynomials.

We compute the Kauffman bracket polynomial of the numerator and denominator closures ofwhere A is a 2-tangle shadow that has at most 4 crossings.

No abstract