General method for calculating degree growth in lattice equations

Develop a general method to calculate degree growth for lattice equations (partial difference equations) defined by rational functions, enabling rigorous computation of exact individual or total degree sequences and algebraic entropy on admissible domains.

Background

The paper motivates the need for a systematic, rigorous approach to computing degree growth in lattice equations as a foundation for algebraic entropy, the most accurate current integrability test in discrete systems. While the authors propose a singularity-based framework for individual degrees, they explicitly note the broader lack of a general method in the field.