# Counting and ordering periodic stationary solutions of lattice Nagumo equations

## TL;DR

This paper investigates the structure of periodic stationary solutions in lattice Nagumo equations, using combinatorial methods to classify and count solutions through equivalence classes and partial orderings.

## Contribution

It introduces a novel approach linking Nagumo lattice solutions to combinatorial objects like necklaces and Lyndon words for classification and enumeration.

## Key findings

- Periodic solutions are classified into equivalence classes.
- A counting method for solutions using combinatorial objects.
- Partial ordering of solutions based on combinatorial structures.

## Abstract

We study the rich structure of periodic stationary solutions of Nagumo reaction diffusion equation on lattices. By exploring the relationship with Nagumo equations on cyclic graphs we are able to divide these periodic solutions into equivalence classes that can be partially ordered and counted. In order to accomplish this, we use combinatorial concepts such as necklaces, bracelets and Lyndon words.