# On the Complexity of Exact Counting of Dynamically Irreducible Polynomials

## TL;DR

This paper presents an efficient algorithm for enumerating sets of quadratic polynomials over finite fields that remain irreducible through iterations and compositions, addressing a complex counting problem in algebraic dynamics.

## Contribution

It introduces a novel algorithm for exact counting of dynamically irreducible quadratic polynomials over finite fields, advancing computational methods in algebraic dynamics.

## Key findings

- Algorithm efficiently enumerates irreducible polynomial sets
- Provides exact counts for dynamically irreducible polynomials
- Enhances understanding of polynomial iteration over finite fields

## Abstract

We give an efficient algorithm to enumerate all sets of $r\ge 1$ quadratic polynomials over a finite field, which remain irreducible under iterations and compositions.