dzhang314 / ZeroOnePolynomials

Software and partial results for the 0-1 Polynomial Conjecture

ZeroOnePolynomials

Definition: Let $R$ be a commutative unital ring. A polynomial $P \in R[x]$ is a 0-1 polynomial if every coefficient of $P$ is either $0_R$ or $1_R$.

0-1 Polynomial Conjecture: Let $P, Q \in \mathbb{R}[x]$ be monic polynomials with nonnegative coefficients. If their product $R(x) \coloneqq P(x) Q(x)$ is a 0-1 polynomial, then $P$ and $Q$ are 0-1 polynomials.

This repository contains high-performance computer programs that test the 0-1 Polynomial Conjecture for small values of $(\deg P, \deg Q)$. Using these programs, I have independently verified that the 0-1 Polynomial Conjecture holds whenever $\deg R \le 45$.