Trees on hyperbolic honeycombs

TL;DR

This paper investigates the properties and growth probabilities of trees constructed on infinite regular lattices in the hyperbolic plane, analyzing how these trees expand and behave at different levels.

Contribution

It introduces a recursive method to analyze the growth and length probabilities of trees on hyperbolic honeycombs, a novel approach in hyperbolic lattice studies.

Findings

Trees exhibit exponential growth in hyperbolic lattices

Probabilities of tree lengths vary with lattice level

Recursive analysis provides insights into tree expansion patterns

Abstract

In the hyperbolic plane there are infinite regular lattices. From a fix vertex of a lattice tree graphs can be constructed recursively to the next layers with edges of the lattice. In this article we examine the properties of the growing of trees and the probabilities of length of trees considering the vertices on level i.