The multiplicative inequality for class degrees via relative transition classes

TL;DR

This paper introduces the concept of class degree for factor codes, extending the degree notion to infinite-to-one cases, and studies how class degrees vary compared to degrees when factor codes are composed.

Contribution

It generalizes the degree concept to class degree for infinite-to-one factors and analyzes its behavior relative to degrees under factor code comparisons.

Findings

Class degree extends the properties of degree to infinite-to-one factors.

The paper provides insights into how class degrees change when factor codes are compared.

It establishes foundational properties of class degrees in symbolic dynamics.

Abstract

Generalizing the notion of the degree of a finite-to-one factor code from a shift of finite type, the class degree of a possibly infinite-to-one factor extends many important properties of degree. In this paper, introducing class degree, we study how class degrees change as two factor codes are, in comparison with degrees.