This repository contains code accompanying the paper Sharp isoperimetric inequalities on the Hamming cube near the critical exponent by Polona Durcik, Paata Ivanisvili and Joris Roos, arXiv:2407.12674.

The code produces provably correct bounds using interval/ball arithmetic relying on FLINT/Arb.

Installation

1. Install a Python 3 distribution (at least 3.9).

2. Install the latest version of python-flint. As of this writing, the latest stable release (0.6.0) lacks the inverse error function, but the function is available in recent pre-releases >=0.7.0a1. To install use:

    pip install python-flint>=0.7.0a1
   

3. Install Git.

4. Clone this repository:

    git clone https://github.com/roos-j/dir24-isoperim.git
   

Usage

To verify all computer-assisted claims in the paper use

python run.py --beta 0.50057 --c 0.997

To save partition data to file use

python run.py --filename partitions.py

To view all command line options run

python run.py -h