Row-constrained effective sets of colourings in the $2$-fold horocyclic tessellations of $\mathbb{H}^2$ are sofic

TL;DR

This paper proves that row-constrained effective sets of colourings in the 2-fold horocyclic tessellations of the hyperbolic plane are sofic, advancing understanding of symbolic dynamics in hyperbolic geometry.

Contribution

It establishes the soficity of row-constrained effective colouring sets in hyperbolic tessellations, a novel result in symbolic dynamics on hyperbolic spaces.

Findings

Effective sets of colourings are sofic under row constraints.

Extends symbolic dynamics theory to hyperbolic tessellations.

Provides new tools for studying hyperbolic tilings.

Abstract

In this article we prove that, restricted to the row-constrained case, effective sets of colourings in the $2$-fold horocyclic tessellations of the hyperbolic plane $\mathbb{H}^2$ are sofic.