Supplement to the article "irreducible polynomials with bounded height"

TL;DR

This paper discusses the probability that the determinant of a random matrix is a perfect square, highlighting its unlikelihood.

Contribution

It provides a probabilistic analysis showing that a random matrix's determinant is unlikely to be a square, contributing to understanding of random matrix properties.

Findings

Determinant of a random matrix is unlikely to be a perfect square

Provides probabilistic bounds on the likelihood of determinants being squares

Enhances understanding of algebraic properties of random matrices

Abstract

We show that the determinant of a random matrix is unlikely to be a square.