The Kauffman brackets for equivalence classes of links

Zeros of the Jones Polynomial are Dense in the Complex Plane

“…The first part is on a formula of computing the Tutte polynomial of signed graphs formed by edge replacements via the chain polynomial [12]. This result generalizes our previous results in [13]. It is worth noting that there are two closely related results in [14] and [15].…”

“…n ] = (X/A) n = (−A −4 ) n . Hence, we have Corollary 2.7 [13] Let G be a connected labeled graph. Let G c be the signed graph obtained from G by replacing each edge a by a positive path with length n a .…”

On Computing Kauffman Bracket Polynomial of Montesinos Links

“…For example, Knotscape [6] computes various link invariants, but only handle small knots. By now, Jones polynomials or Kauffman bracket polynomials of many link families have been computed, say, (m, n)-torus knot [4], pretzel links [7][8][9], rational links [10,11], etc. In recent years, the computer algebra (Maple) techniques were used to calculate link polynomials for various link families, see [7,[12][13][14].…”

“…Proposition 3.2 can be obtained by combining Eqs. (3) and (7) in [9]. Actually it can also be obtained from the spanning tree expansion for Q [G] in [16].…”