Geodesic
Characterization of Lattices Induced by (extended) Chip Firing Games
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001) (2001).

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

The Chip Firing Game (CFG) is a discrete dynamical model used in physics, computer science and economics. It is known that the set of configurationsreachable from an initial configuration (this set is called the \textitconfiguration space) can be ordered as a lattice. We first present a structural result about this model, which allows us to introduce some useful tools for describing those lattices. Then we establish that the class of lattices that are the configuration space of a CFG is strictly between the class of distributive lattices and the class of upper locally distributive (or ULD) lattices. Finally we propose an extension of the model, the \textitcoloured Chip Firing Game, which generates exactly the class of ULD lattices. 
@article{DMTCS_2001_special_246_a0,
     author = {Magnien, Cl\'emence and Phan, Ha Duong and Vuillon, Laurent},
     title = {Characterization of {Lattices} {Induced} by (extended) {Chip} {Firing} {Games}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)},
     year = {2001},
     doi = {10.46298/dmtcs.2277},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2277/}
}
TY  - JOUR
AU  - Magnien, Clémence
AU  - Phan, Ha Duong
AU  - Vuillon, Laurent
TI  - Characterization of Lattices Induced by (extended) Chip Firing Games
JO  - Discrete mathematics & theoretical computer science
PY  - 2001
VL  - DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2277/
DO  - 10.46298/dmtcs.2277
LA  - en
ID  - DMTCS_2001_special_246_a0
ER  - 
%0 Journal Article
%A Magnien, Clémence
%A Phan, Ha Duong
%A Vuillon, Laurent
%T Characterization of Lattices Induced by (extended) Chip Firing Games
%J Discrete mathematics & theoretical computer science
%D 2001
%V DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2277/
%R 10.46298/dmtcs.2277
%G en
%F DMTCS_2001_special_246_a0
Magnien, Clémence; Phan, Ha Duong; Vuillon, Laurent. Characterization of Lattices Induced by (extended) Chip Firing Games. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001) (2001). doi : 10.46298/dmtcs.2277. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2277/

Cité par Sources :