Voltage graphs, weight systems and odd symmetry Original Research Article

We present combinatorial constructions of the weight systems associated with Vassiliev link invariants by means of natural maps from the space of equivalence classes of Chinese characters to the spaces of marked diagrams. The weight systems coming from those maps are described. In particular, we establish that all the weight systems coming from the so-called voltage graphs come also from the classical Lie algebras gl(n) and so(n). We analyze the combinatorial difficulties arising in attempt to answer the noninvertibility conjecture (NIC) for Vassiliev knot invariants.