Strongly nilpotent automorphisms are Pascal finite

Abstract

We compare two classes of polynomial automorphisms, strongly nilpotent and Pascal finite. We conclude that every strongly nilpotent automorphism is a Pascal finite one, but not vice versa. We observe that Nagata's automorphism is Pascal finite, but not strongly nilpotent. Considering Vasyunin example leads us to conclusion that not every quadratic polynomial automorphism is Pascal finite.