@conference{10902/29689,
year = {2011},
url = {https://hdl.handle.net/10902/29689},
abstract = {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 pseudoline arrangements with contacts supported by a given network. In this paper, we construct the "brick polytope'' of a network, obtained as the convex hull of the "brick vectors'' associated to each pseudoline arrangement supported by the network. We characterize its vertices, describe its faces, and decompose it as a Minkowski sum of simpler polytopes. Our brick polytopes include Hohlweg and Lange's many realizations of the associahedron, which arise as brick polytopes of certain well-chosen networks.},
organization = {Research supported by grant MTM2008-04699-C03-02 of the Spanish Ministry of Education and Science.},
publisher = {Discrete mathematics & theoretical computer science, 2011, 777-788},
title = {The brick polytope of a sorting network},
author = {Pilaud, Vincent and Santos, Francisco},
}