The Jacobian Conjecture as a problem in combinatorics
نویسنده
چکیده
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 JH = 0. Other special results are also derived. We pose a combinatorial statement which would give a complete proof the Jacobian Conjecture.
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