On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture
Abstract
In this paper we describe a parallel algorithm for generating all nonisomorphic rank 3 simple matroids with a given multiplicity vector. We apply our implementation in the high performance computing version of GAP to generate all rank 3 simple matroids with at most 14 atoms and an integrally 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.
Citation
Barakat , M , Behrends , R , Jefferson , C , Kühne , L & Leuner , M 2021 , ' On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture ' , SIAM Journal on Discrete Mathematics , vol. 35 , no. 2 , pp. 1201-1223 . https://doi.org/10.1137/19M1296744
Publication
SIAM Journal on Discrete Mathematics
Status
Peer reviewed
ISSN
0895-4801Type
Journal article
Description
This work is a contribution to Project II.1 of SFB-TRR 195 "Symbolic Tools in Mathematics and their Application" funded by Deutsche Forschungsgemeinschaft (DFG). The fourth author was supported by ERC StG 716424 - CASe, a Minerva Fellowship of the Max Planck Society and the Studienstiftung des deutschen Volkes.Collections
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