On the Generation of Rank 3 Simple Matroids with an Application to Terao's Freeness Conjecture
Barakat M, Behrends R, Jefferson C, Kühne L, Leuner M (2021)
SIAM Journal on Discrete Mathematics 35(2): 1201-1223.
Zeitschriftenaufsatz
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Autor*in
Barakat, Mohamed;
Behrends, Reimer;
Jefferson, Christopher;
Kühne, LukasUniBi 
;
Leuner, Martin
;
Leuner, MartinEinrichtung
Abstract / Bemerkung
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.
Stichworte
rank 3 simple matroids;
integrally splitting characteristic polynomial;
Terao's freeness conjecture recursive iterator;
tree-iterator;
leaf-iterator;
iterator of leaves of rooted tree
Erscheinungsjahr
2021
Zeitschriftentitel
SIAM Journal on Discrete Mathematics
Band
35
Ausgabe
2
Seite(n)
1201-1223
ISSN
0895-4801
eISSN
1095-7146
Page URI
https://pub.uni-bielefeld.de/record/2982145
Zitieren
Barakat M, Behrends R, Jefferson C, Kühne L, Leuner M. On the Generation of Rank 3 Simple Matroids with an Application to Terao's Freeness Conjecture. SIAM Journal on Discrete Mathematics. 2021;35(2):1201-1223.
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, 35(2), 1201-1223. https://doi.org/10.1137/19M1296744
Barakat, Mohamed, Behrends, Reimer, Jefferson, Christopher, Kühne, Lukas, and Leuner, Martin. 2021. “On the Generation of Rank 3 Simple Matroids with an Application to Terao's Freeness Conjecture”. SIAM Journal on Discrete Mathematics 35 (2): 1201-1223.
Barakat, M., Behrends, R., Jefferson, C., Kühne, L., and Leuner, M. (2021). On the Generation of Rank 3 Simple Matroids with an Application to Terao's Freeness Conjecture. SIAM Journal on Discrete Mathematics 35, 1201-1223.
Barakat, M., et al., 2021. On the Generation of Rank 3 Simple Matroids with an Application to Terao's Freeness Conjecture. SIAM Journal on Discrete Mathematics, 35(2), p 1201-1223.
M. Barakat, et al., “On the Generation of Rank 3 Simple Matroids with an Application to Terao's Freeness Conjecture”, SIAM Journal on Discrete Mathematics, vol. 35, 2021, pp. 1201-1223.
Barakat, M., Behrends, R., Jefferson, C., Kühne, L., Leuner, M.: On the Generation of Rank 3 Simple Matroids with an Application to Terao's Freeness Conjecture. SIAM Journal on Discrete Mathematics. 35, 1201-1223 (2021).
Barakat, Mohamed, Behrends, Reimer, Jefferson, Christopher, Kühne, Lukas, and Leuner, Martin. “On the Generation of Rank 3 Simple Matroids with an Application to Terao's Freeness Conjecture”. SIAM Journal on Discrete Mathematics 35.2 (2021): 1201-1223.
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