This talk is a report on joint work with A Vaintrob [arXiv:math.CO/0109104] and [arXiv:math.GT/0111102]. It
is organised as follows. We begin by recalling how the classical
Matrix-Tree Theorem relates two different expressions for the lowest
degree coefficient of the Alexander–Conway polynomial of a
link. We then state our formula for the lowest degree coefficient of an
algebraically split link in terms of Milnor's triple linking numbers.
We explain how this formula can be deduced from a determinantal expression
due to Traldi and Levine by means of our Pfaffian Matrix-Tree Theorem
[arXiv:math.CO/0109104]. We
also discuss the approach via finite type invariants, which allowed us in
[arXiv:math.GT/0111102]
to obtain the same result directly from some properties of the
Alexander-Conway weight system. This approach also gives similar results
if all Milnor numbers up to a given order vanish.
