Strongly nilpotent automorphisms are Pascal finite

TL;DR

The paper compares classes of polynomial automorphisms, establishing that strongly nilpotent automorphisms are Pascal finite, with examples illustrating the distinctions and limitations of these classes.

Contribution

It proves that all strongly nilpotent automorphisms are Pascal finite and provides examples showing the boundaries of this relationship.

Findings

Every strongly nilpotent automorphism is Pascal finite.

Nagata's automorphism is Pascal finite but not strongly nilpotent.

Not all quadratic polynomial 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.