https://github.com/dzhang314/zeroonepolynomials

Software and partial results for the 0-1 Polynomial Conjecture
https://github.com/dzhang314/zeroonepolynomials

Last synced: about 1 month ago
JSON representation

Software and partial results for the 0-1 Polynomial Conjecture

• Host: GitHub
• URL: https://github.com/dzhang314/zeroonepolynomials
• Owner: dzhang314
• License: mit
• Created: 2023-05-13T01:21:34.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2024-08-23T02:04:22.000Z (4 months ago)
• Last Synced: 2024-08-23T03:22:37.963Z (4 months ago)
• Language: C++
• Homepage: https://mathoverflow.net/questions/339137/why-do-polynomials-with-coefficients-0-1-like-to-have-only-factors-with-0-1
• Size: 116 MB
• Stars: 0
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

Awesome Lists containing this project

README

        
# 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](https://mathoverflow.net/questions/339137/why-do-polynomials-with-coefficients-0-1-like-to-have-only-factors-with-0-1):** 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 $\deg R \le 45$.