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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 $t^{-1} - 1 + t$.

Suppose that $K$ is an alternating knot.

Conjecture: 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?

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?

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 $t^{-1} - 1 + t$.

Suppose that $K$ is an alternating knot.

CONJECTURE: The sequence of absolute values of the coefficients is unimodal. Specifically,

if $\Delta \sb K(t) = \sum\sb i a\sb i t^i$" />, then $|a\sb 0| \ge |a\sb 1| \ge |a\sb 2| \ge \cdots$" />

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

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 $t^{-1} - 1 + t$.

Suppose that $K$ is an alternating knot.

Conjecture: 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?