Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the generation of rank 3 simple matroids with an application to
  Terao's freeness conjecture   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.

19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org