Article - post-print
We use Polyak's skein relation to give a new proof that Milnor's string link homotopy invariants are finite type invariants, and to develop a recursive relation for their associated weight systems. We show that the obstruction to the triviality of these weight systems is the presence of a certain kind of spanning tree in the intersection graph of a chord diagram.
Mellor, B., 2008: Weight Systems for Milnor Invariants. J. Knot Theory Ramif., 17.2, 213-230, arXiv:math/0501280.