Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A universality theorem for allowable sequences with applications   Order types are a well known abstraction of combinatorial properties of a
point set. By Mn\"ev's universality theorem for each semi-algebraic set $V$
there is an order type with a realization space that is \emph{stably
equivalent} to $V$. We consider realization spaces of \emph{allowable
sequences}, a refinement of order types. We show that the realization spaces of
allowable sequences are \emph{universal} and consequently deciding the
realizability is complete in the \emph{existential theory of the reals} (\ER).
This result holds even if the realization space of the order type induced by
the allowable sequence is non-empty. Furthermore, we argue that our result is a
useful tool for further geometric reductions. We support this by giving
\ER-hardness proofs for the realizability of abstract convex geometries and for
the recognition problem of visibility graphs of polygons with holes using the
hardness result for allowable sequences. This solves two longstanding open
problems.

16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex