A subperiodic tree whose intermediate branching number is strictly less than the lower intermediate growth rate

TL;DR

This paper constructs a specific subperiodic tree demonstrating that its intermediate branching number can be strictly less than its lower intermediate growth rate, providing a counterexample to a question posed by Amir and Yang in 2022.

Contribution

The paper presents the first explicit example of a subperiodic tree with intermediate branching number less than its lower intermediate growth rate, answering a previously open question.

Findings

Counterexample to Amir and Yang's question (2022)

Intermediate branching number can be strictly less than lower intermediate growth rate

Advances understanding of growth properties in subperiodic trees

Abstract

We construct an example of a subperiodic tree whose intermediate branching number is strictly less than the lower intermediate growth rate. This answers a question of Amir and Yang (2022) in the negative.