Hipster Tree Growth Rates

TL;DR

This paper studies a special class of rooted trees called hipster trees, characterized by having no nontrivial automorphisms, and analyzes their growth rates through generating functions.

Contribution

It introduces the concept of hipster trees and provides bounds on their exponential growth rates by approximating their generating functions.

Findings

Bounds on exponential growth rates of hipster trees

Characterization of hipster trees via subtree isomorphisms

Approximate generating functions for counting hipster trees

Abstract

A plane rooted tree is called a hipster tree if it has no nontrivial automorphisms. Equivalently, a tree is a hipster tree if no two siblings have isomorphic subtrees. We impose the hipster condition on various classes of rooted trees. By approximating the generating function for the number of such trees, we obtain bounds on their exponential growth rates.