A PROOF OF THE MELVIN–MORTON CONJECTURE AND FEYNMAN DIAGRAMS
The Melvin–Morton conjecture says how the Alexander–Conway knot invariant function can be read from the coloured Jones function. It has been proved by D. Bar-Natan and S. Garoufalidis. They reduced the conjecture to a statement about weight systems. The proof of the latter is the most difficult part of their paper. We give a new proof of the statement based on the Feynman diagram description of the primitive space of the Hopf algebra of chord diagrams.