# Tuples of polynomials over finite fields with pairwise coprimality conditions

## TL;DR

This paper estimates the count of polynomial tuples over finite fields satisfying pairwise coprimality conditions and extends the results to Dedekind domains with finite norms.

## Contribution

It generalizes the enumeration of coprime polynomial tuples from finite fields to Dedekind domains with finite norms.

## Key findings

- Derived explicit estimates for polynomial tuples over finite fields.
- Extended the enumeration framework to Dedekind domains.
- Provided a unified approach for coprimality conditions in algebraic structures.

## Abstract

Let $q$ be a prime power. We estimate the number of tuples of degree bounded monic polynomials $(Q_1,\ldots,Q_v) \in (\mathbb{F}_q[z])^v$ that satisfy given pairwise coprimality conditions. We show how this generalises from monic polynomials in finite fields to Dedekind domains with finite norms.