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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 7 > No. 1


Taylor series coefficients of the HP-polynomial as an invariant for links in the solid torus

PP: 203-208
K. Bataineh,
We show that the coe▒cients of a reformulation of a Taylor series expansion of the Hoste and Pryzyticki polynomial are Vassiliev invariants. We also show that many other reformulations of the Taylor series expansion have coe▒cients that are Vassiliev invariants. We charecterize the »rst two coe▒cients b1 0(t) and bL 1 (t) for one of these expan- sions. Moreover, the second coe▒cient bL 1 (t); which is a type-one Vassiliev invariant, is given two explicit computational formulas, which are easy to calculate. bL 1 (t) is used to give a lower bound for the crossing number of a knot of zero winding number in the solid torus.

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