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Younger mates and the Jacobian conjecture

Authors: Charles Ching-an Cheng, James H. McKay and Stuart Sui Sheng Wang
Journal: Proc. Amer. Math. Soc. 123 (1995), 2939-2947
MSC: Primary 14E09; Secondary 13B25
MathSciNet review: 1257100
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Abstract: Let $ F,G \in \mathbb{C}[x,y]$. If the Jacobian determinant of F and G is 1, then G is said to be a Jacobian mate of F. If, in addition, G has degree less than that of F, then G is said to be a younger mate of F. In this paper, a necessary and sufficient condition is given for a polynomial to have a younger mate. This also gives rise to a formula for the younger mate if it exists. Furthermore, a conjecture concerning the existence of a younger mate is shown to be equivalent to the Jacobian conjecture.

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Keywords: Jacobian conjecture, Jacobian hypothesis, Jacobian mate, younger mate, automorphism, automorphism pair, Sylvester matrix, resultant, Newton polygon
Article copyright: © Copyright 1995 American Mathematical Society

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