A relation between the LG polynomial and the Kauffman polynomial (Q876537)

The authors consider the 2-variable link polynomials of Links and Gould, \(LG_L(t_0,t_1)\), of Kauffman, \(F_L(a,z)\), and the so-called Dubrovnik polynomial, \(Y_L(a,z)\) of an oriented link \(L\) in \(S^3\). The reduced polynomial \(LG_L(t,t)(= KLG_L(t))\) is proved to be equal to suitable reductions of \(F_L\) and \(Y_L\). Using a result of Thistlethwaite on \(F_L (a,z)\) this shows that the crossing number of an adequate link diagram is obtained by \(LG_L\). (A reduced alternating diagram is adequate.) Also the determinant of \(L\) is determined by \(KLG\).