The Jacobian Conjecture as a problem in combinatorics

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

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

References in corpus (1)

• Legendre Transform, Hessian Conjecture and Tree Formula

Cited by in corpus (1)

• The Jacobian Conjecture, together with Specht and Burnside-type problems