# Asymptotic growth rate of square grids dominating sets: a symbolic dynamics approach

## TL;DR

This paper establishes the existence of an asymptotic growth rate for dominating sets on large rectangular grids and provides algorithms and bounds for computing these rates.

## Contribution

It introduces a symbolic dynamics approach to prove growth rate existence and offers algorithms to compute and bound these rates for various dominating set variants.

## Key findings

- Existence of asymptotic growth rates for dominating sets on large grids
- Algorithms for computing growth rates of dominating sets
- Bounds on growth rates obtained via computer programs

## Abstract

In this text, we prove the existence of an asymptotic growth rate of the number of dominating sets (and variants) on finite rectangular grids, when the dimensions of the grid grow to infinity. Moreover, we provide, for each of the variants, an algorithm which computes the growth rate. We also give bounds on these rates provided by a computer program.