TY - JOUR
T1 - Sandpile models and lattices
T2 - A comprehensive survey
AU - Goles, Éric
AU - Latapy, Matthieu
AU - Magnien, Clémence
AU - Morvan, Michel
AU - Phan, Ha Duong
PY - 2004/8/30
Y1 - 2004/8/30
N2 - Starting from some studies of (linear) integer partitions, we noticed that the lattice structure is strongly related to a large variety of discrete dynamical models, in particular sandpile models and chip firing games. After giving an historical survey of the main results which appeared about this, we propose a unified framework to explain the strong relationship between these models and lattices. In particular, we show that the apparent complexity of these models can be reduced, by showing the possibility of simplifying them, and we show how the known lattice properties can be deduced from this.
AB - Starting from some studies of (linear) integer partitions, we noticed that the lattice structure is strongly related to a large variety of discrete dynamical models, in particular sandpile models and chip firing games. After giving an historical survey of the main results which appeared about this, we propose a unified framework to explain the strong relationship between these models and lattices. In particular, we show that the apparent complexity of these models can be reduced, by showing the possibility of simplifying them, and we show how the known lattice properties can be deduced from this.
KW - Chip firing games
KW - Discrete dynamical models
KW - Integer partitions
KW - Lattices
KW - Sandpile models
UR - http://www.scopus.com/inward/record.url?scp=3843087248&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2004.03.019
DO - 10.1016/j.tcs.2004.03.019
M3 - Article
AN - SCOPUS:3843087248
SN - 0304-3975
VL - 322
SP - 383
EP - 407
JO - Theoretical Computer Science
JF - Theoretical Computer Science
IS - 2
ER -