Notes for AKT-090917-2/0:27:14

Rearranging the skein relation, we see that:

[math]\displaystyle{ J(\doublepoint)=x(...) }[/math]

Analogously,

[math]\displaystyle{ J(\doublepoint ... \doublepoint)=x^{n+1}(...) }[/math]

for n+1 double points. In particular, the coefficient of [math]\displaystyle{ x^n }[/math], [math]\displaystyle{ J_n }[/math], will be zero when evaluated on a knot with [math]\displaystyle{ k+1 }[/math] double points.