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In 2002 Haviv gave a way of assigning Lie tensors to directed trivalentgraphs. Weight systems on oriented chord idagrams modulo 6T can then beconstructed from such tensors. In this paper we give explicit combinatorialformulas of weight systems using Manin triples constrcted from classical Liealgebras. We then compose these oriented weight systems with the averaging mapto get weight systems on unoriented chord diagrams and show that they are thesame as the ones obtained by Bar-Natan in 1991. In the last section we carryout calculations on certain examples.

Combinatorial Formulas for Classical Lie Weight Systems on Arrow Diagrams