Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The brick polytope of a sorting network   The associahedron is a polytope whose graph is the graph of flips on
triangulations of a convex polygon. Pseudotriangulations and
multitriangulations generalize triangulations in two different ways, which have
been unified by Pilaud and Pocchiola in their study of flip graphs on
pseudoline arrangements with contacts supported by a given sorting network.
  In this paper, we construct the brick polytope of a sorting network, obtained
as the convex hull of the brick vectors associated to each pseudoline
arrangement supported by the network. We combinatorially characterize the
vertices of this polytope, describe its faces, and decompose it as a Minkowski
sum of matroid polytopes.
  Our brick polytopes include Hohlweg and Lange's many realizations of the
associahedron, which arise as brick polytopes for certain well-chosen sorting
networks. We furthermore discuss the brick polytopes of sorting networks
supporting pseudoline arrangements which correspond to multitriangulations of
convex polygons: our polytopes only realize subgraphs of the flip graphs on
multitriangulations and they cannot appear as projections of a hypothetical
multiassociahedron.

26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph