Geodesic
Chip-Firing And A Devil's Staircase
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009).

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

The devil's staircase ― a continuous function on the unit interval $[0,1]$ which is not constant, yet is locally constant on an open dense set ― is the sort of exotic creature a combinatorialist might never expect to encounter in "real life.'' We show how a devil's staircase arises from the combinatorial problem of parallel chip-firing on the complete graph. This staircase helps explain a previously observed "mode locking'' phenomenon, as well as the surprising tendency of parallel chip-firing to find periodic states of small period. 
@article{DMTCS_2009_special_256_a15,
     author = {Levine, Lionel},
     title = {Chip-Firing {And} {A} {Devil's} {Staircase}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)},
     year = {2009},
     doi = {10.46298/dmtcs.2693},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2693/}
}
TY  - JOUR
AU  - Levine, Lionel
TI  - Chip-Firing And A Devil's Staircase
JO  - Discrete mathematics & theoretical computer science
PY  - 2009
VL  - DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2693/
DO  - 10.46298/dmtcs.2693
LA  - en
ID  - DMTCS_2009_special_256_a15
ER  - 
%0 Journal Article
%A Levine, Lionel
%T Chip-Firing And A Devil's Staircase
%J Discrete mathematics & theoretical computer science
%D 2009
%V DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2693/
%R 10.46298/dmtcs.2693
%G en
%F DMTCS_2009_special_256_a15
Levine, Lionel. Chip-Firing And A Devil's Staircase. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009). doi : 10.46298/dmtcs.2693. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2693/

Cité par Sources :