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On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture
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dc.contributor.author | Barakat, M. | |
dc.contributor.author | Behrends, R. | |
dc.contributor.author | Jefferson, C. | |
dc.contributor.author | Kühne, L. | |
dc.contributor.author | Leuner, M. | |
dc.date.accessioned | 2021-07-14T14:30:24Z | |
dc.date.available | 2021-07-14T14:30:24Z | |
dc.date.issued | 2021-06-08 | |
dc.identifier | 274949538 | |
dc.identifier | 14604745-cba8-4204-9812-082bc2581dae | |
dc.identifier | 85108739370 | |
dc.identifier | 000674142200029 | |
dc.identifier.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 | en |
dc.identifier.issn | 0895-4801 | |
dc.identifier.other | RIS: urn:F6460CC4DDCCFEED903DC2359BD34982 | |
dc.identifier.other | ORCID: /0000-0003-2979-5989/work/96817381 | |
dc.identifier.uri | https://hdl.handle.net/10023/23563 | |
dc.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. | en |
dc.description.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. | |
dc.format.extent | 23 | |
dc.format.extent | 1309855 | |
dc.language.iso | eng | |
dc.relation.ispartof | SIAM Journal on Discrete Mathematics | en |
dc.subject | ArangoDB | en |
dc.subject | Integrally splitting characteristic polynomial | en |
dc.subject | Iterator of leaves of rooted tree | en |
dc.subject | Leaf-iterator | en |
dc.subject | NoSQL database | en |
dc.subject | Parallel evaluation of recursive iterator | en |
dc.subject | Priority queue | en |
dc.subject | Rank 3 simple matroids | en |
dc.subject | Recursive iterator | en |
dc.subject | Terao's freeness conjecture | en |
dc.subject | Tree-iterator | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. School of Computer Science | en |
dc.contributor.institution | University of St Andrews. Centre for Research into Equality, Diversity & Inclusion | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.contributor.institution | University of St Andrews. St Andrews GAP Centre | en |
dc.identifier.doi | https://doi.org/10.1137/19M1296744 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | https://arxiv.org/pdf/1907.01073 | en |
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