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The Jacobian Conjecture as a problem in combinatorics

David Wright
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Abstract

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 $JH^{3}=0$. Other special results are also derived. We pose a combinatorial statement which would give a complete proof the Jacobian Conjecture.

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BibTeXRIS

David Wright. 2006-03-22. The Jacobian Conjecture as a problem in combinatorics. https://arxiv.org/abs/math/0511214

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