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On the Generation of Rank
Mohamed Barakat, Reimer Behrends, Christopher Jefferson, Lukas Kühne and Martin Leuner
Abstract
In this paper, we describe a parallel algorithm for generating all non-isomorphic rank
We apply our implementation in the HPC version of GAP to generate all rank
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
Another database query proves that Terao's freeness conjecture is true for rank
- Received:
- 28.08.20
- Published:
- 28.08.20
- MSC Codes:
- 05B35, 52C35, 32S22, 68R05, 68W10
- Keywords:
- rank $3$ simple matroids, integrally splitting characteristic polynomial, Terao's freeness conjecture, recursive iterator, noSQL database