Generation of Matroids

This page presents an application of the paper:

Mohamed Barakat, Reimer Behrends, Christoper Jefferson, Lukas Kühne, and Martin Leuner: On the generation of rank 3 simple matroids with an application to Terao’ freeness conjecture

In: SIAM journal on discrete mathematics, 35 (2021) 2, p. 1201-1223

MIS-Preprint: 88/2020 DOI: 10.1137/19M1296744 ARXIV: https://arxiv.org/abs/1907.01073 CODE: https://mathrepo.mis.mpg.de/GenerationOfMatroids

The main contribution of this article is a large scale generation of a certain class of matroids in HPC-GAP. Subsequently, we stored these matroids in a publicly availabel Arango DB database: https://matroid.mathematik.uni-siegen.de. This enabled us to answer the following question:

• What is the smallest number \(n\) of atoms of a representable rank \(3\) matroid which is divisionally free but not inductively free?

The code is presented as a Jupyter notebook based on the Julia package CapAndHomalg. It can be downloaded here: MatroidGeneration.ipynb.

You can run the notebook online by clicking the binder badge below.

Project page created: 19/10/2020

Code contributors: Mohamed Barakat, Lukas Kühne

Jupyter Notebook written by: Mohamed Barakat, 17/07/2020

Software used: Julia 1.5.2 and GAP 4.11.0

Corresponding author of this page: Lukas Kühne, lukas.kuhne@mis.mpg.de