The Jacobian Conjecture as a problem in combinatorics

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The Jacobian Conjecture has been reduced to the symmetric homogeneous case. In this paper we give an inversion formula for the symmetric case and relate it to a combinatoric structure called the Grossman-Larson Algebra. We use these tools to prove the symmetric Jacobian Conjecture for the case F=X-H with H homogeneous and JH³=0. Other special results are also derived. We pose a combinatorial statement which would give a complete proof the Jacobian Conjecture.