# On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture

@inproceedings{Barakat2019OnTG, title={On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture}, author={Mohamed Barakat and Reimer Behrends and Christopher Jefferson and Lukas Kuhne and Martin Leuner}, year={2019} }

In this paper we describe a parallel algorithm for generating all non-isomorphic rank $3$ simple matroids with a given multiplicity vector. We apply our implementation in the HPC version of GAP to generate all rank $3$ simple matroids with at most $14$ atoms and a splitting characteristic polynomial. We have stored the resulting matroids alongside with various useful invariants in a publicly available, ArangoDB-powered database. As a byproduct we show that the smallest divisionally free rank $3… CONTINUE READING

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