Younger mates and the Jacobian conjecture

Cheng, Charles Ching-an; McKay, James H.; Wang, Stuart Sui Sheng

doi:10.1090/S0002-9939-1995-1257100-4

Younger mates and the Jacobian conjecture
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by Charles Ching-an Cheng, James H. McKay and Stuart Sui Sheng Wang PDF

Proc. Amer. Math. Soc. 123 (1995), 2939-2947 Request permission

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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