Jones Polynomial For Knots And Links And Their Achirality

We already know that Laurent polynomial an integral coefficients Δ(t) is a Alexander polynomial if and only(1)Δ(1)=1(2) Δ(t)=Δ(t-1).What about the relations between Jones polynomial and Laurent polynomial?Recently, some scholars has discuss a situation that degree number is less than and equal to5,it promotes the situation that degree number is6,7with constant term is0.This paper discusses the relation between an integral coefficients Laurent polynomial with a degree number is8,9and Jones polynomial by the theory of matrix and polynomial and get the main results; Some scholars discussed the relation between Jones polynomial and Tutte polynomial, by the means of general to special,we get the Jones polynomials of pretzel knot P(c1,c2,c3) when c1,c2, c3take values classify.We give an easy proof method of achirality of P(c1,c2,1) and P(c1,1,c3);Some scholars introduced a family knot P(xl,x2,…,xn;y1,y2,…,yn)that is similar to pretzel knot but more complex.This paper discuss the Jones polynomials of P(x1,x2;y1, y2),when x1,x2,y1, y2take values classify by the means of general to special.