2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156364We 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.13 pages, 8 figures. Latest version has minor technical changesGeometric TopologyCombinatorics57M27text