English

The Jacobian Conjecture as a problem in combinatorics

Combinatorics 2007-05-23 v2 Commutative Algebra Algebraic Geometry

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=XHF=X-H with HH homogeneous and JH3=0JH^{3}=0. Other special results are also derived. We pose a combinatorial statement which would give a complete proof the Jacobian Conjecture.

Keywords

Cite

@article{arxiv.math/0511214,
  title  = {The Jacobian Conjecture as a problem in combinatorics},
  author = {David Wright},
  journal= {arXiv preprint arXiv:math/0511214},
  year   = {2007}
}

Comments

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