Normalize the Alexander polynomial (in $t$) so that the positive and negative exponents are balanced. For example in the Conway normalization, make the substitution $z = t^{1/2} - t^{-1/2}$. The trefoil gives $t^{-1} - 1 + t$.

Conjecture:Suppose that $K$ is an alternating knot. Then the sequence of absolute values of the coefficients is unimodal. Specifically, if $\Delta_K(t) = \sum_i a_i t^i$, then $|a_0| \ge |a_1| \ge |a_2| \ge \cdots$.

This is a conjecture due to Murasugi, I believe. Where is it written? Has this been proved or disproved?