On page 9 of Kauffman's Formal Knot theory, Kauffman claims



> 
> The Alexander-Conway Polynomial is a true refinement of the Alexander Polynomial. Because it is defined absolutely (rather than up to sign and powers of variables) it is capable of distinguishing many links from their mirror images - a capability not available to the Alexander polynomial
> 
> 
> 


Does anybody know of any examples of this happening? Or when two knots have the same Alexander polynomial but different Alexander-Conway polynomials?



Are there knots that can be distinguished by the Alexander-Conway polynomial, but not the Alexander polynomial?
Let $\overline{L}$ denote the mirror image of a link $L$. The (reduced) Alexander-Conway polynomial $D\_L(t)$ of an $n$-component link $L$ satisfies $D\_{\overline{L}}(t)=(-1)^{n+1}D\_L(t)$. More generally, the multivariable potential function $\nabla\_L(t\_1,\ldots,t\_n)$ also satisfies $\nabla\_{\overline{L}}(t\_1,\ldots,t\_n)=(-1)^{n+1}\nabla\_L(t\_1,\ldots,t\_n)$. So you can use these sign-refined versions to distinguish links from their mirror images for links with an even number of components.


