Date of Award


Degree Type


Degree Name

Master of Science



Major Professor

James R. Conant

Committee Members

Don B. Hinton, Morwen B. Thistlethwaite


We disprove the conjecture that if K is amphicheiral and K is concordant to K', then CK'(z)CK'(iz)CK\(z2) is a perfect square inside the ring of power series with integer coefficients. The Alexander polynomial of (p,q)-torus knots are found to be of the form AT(p,q)(t)= (f(tq))/(f(t)) where f(t)=1+t+t2+...+tp-1. Also, for (pn,q)-torus knots, the Alexander polynomial factors into the form AT(pn ,q)=f(t)f(tp)f(tp2 )...f(tpn-2 )f(tpn-1 ). A new conversion from the Alexander polynomial to the Conway polynomial is discussed using the Lucas polynomial. This result is used to show that the Conway polynomial of (2n,q)-torus knots are of the form CT(2n ,q)(z)=K1K2...Kn where K1=Fq(z), Fq(z) being the Fibonacci polynomial, and Ki(z)=Ki-1(√z4+4z2).

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