Geodesic
The brick polytope of a sorting network
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

Voir la notice de l'article provenant de la source Episciences

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. 
@article{DMTCS_2011_special_260_a65,
     author = {Pilaud, Vincent and Santos, Francisco},
     title = {The brick polytope of a sorting network},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)},
     year = {2011},
     doi = {10.46298/dmtcs.2952},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2952/}
}
TY  - JOUR
AU  - Pilaud, Vincent
AU  - Santos, Francisco
TI  - The brick polytope of a sorting network
JO  - Discrete mathematics & theoretical computer science
PY  - 2011
VL  - DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2952/
DO  - 10.46298/dmtcs.2952
LA  - en
ID  - DMTCS_2011_special_260_a65
ER  - 
%0 Journal Article
%A Pilaud, Vincent
%A Santos, Francisco
%T The brick polytope of a sorting network
%J Discrete mathematics & theoretical computer science
%D 2011
%V DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2952/
%R 10.46298/dmtcs.2952
%G en
%F DMTCS_2011_special_260_a65
Pilaud, Vincent; Santos, Francisco. The brick polytope of a sorting network. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2952. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2952/

Cité par Sources :