An oriented state model for the Jones polynomial and its applications alternating links

In this paper, we define a polynomial invariant of regular isotopy, GL, for oriented knot and link diagrams L. From GL by multiplying it by a normalizing factor, we obtain an ambient isotopy invariant, NL, for oriented knots and links. We compare the polynomial NL with the original Jones polynomial and with the normalized bracket polynomial. We show that the polynomial NL yields the Jones polynomial and the normalized bracket polynomial. As examples, we give the polynomial GL of some knot and link diagrams and compute the polynomial GL for torus links of type (2, n), and applying computer algebra (MAPLE) techniques, we calculate the polynomial GL of torus links of type (2, n). Furthermore we give its applications to alternating links.