Papers › On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture
On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture
Mohamed Barakat, Reimer Behrends, Christopher Jefferson, Lukas Kühne, Martin Leuner
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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 arrangement which is not inductively free has 14 hyperplanes and exists in all characteristics distinct from 2 and 5. Another database query proves that Terao's freeness conjecture is true for rank 3 arrangements with 14 hyperplanes in any characteristic.
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