The Jacobian Conjecture as a problem in combinatorics

Details The Jacobian Conjecture as a problem in combinatorics The Jacobian Conjecture as a problem in combinatorics

2005-11-08

arxiv.org/abs/math/0511214v2

Mathematics

Combinatorics

19 pages; submitted for publication in an upcoming volume honoring Masayoshi Miyanishi

Scientific paper

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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