A generalization of the Shestakov-Umirbaev inequality

TL;DR

This paper extends the Shestakov-Umirbaev inequality, a key tool in solving the tame generators conjecture, broadening its applicability in algebraic research.

Contribution

It provides a generalized form of the inequality, enhancing its utility in algebraic and polynomial automorphism studies.

Findings

Generalized the Shestakov-Umirbaev inequality

Improved tools for analyzing polynomial automorphisms

Facilitated progress on the tame generators conjecture

Abstract

We give a generalization of the Shestakov-Umirbaev inequality which plays an important role in their solution of the tame generators conjecture.