Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On topological and geometric $(19_4)$ configurations   An $(n_k)$ configuration is a set of $n$ points and $n$ lines such that each
point lies on $k$ lines while each line contains $k$ points. The configuration
is geometric, topological, or combinatorial depending on whether lines are
considered to be straight lines, pseudolines, or just combinatorial lines. The
existence and enumeration of $(n_k)$ configurations for a given $k$ has been
subject to active research. A current front of research concerns geometric
$(n_4)$ configurations: it is now known that geometric $(n_4)$ configurations
exist for all $n \ge 18$, apart from sporadic exceptional cases. In this paper,
we settle by computational techniques the first open case of $(19_4)$
configurations: we obtain all topological $(19_4)$ configurations among which
none are geometrically realizable.

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess