Sandpile models and lattices: A comprehensive survey

Éric Goles, Matthieu Latapy, Clémence Magnien, Michel Morvan, Ha Duong Phan

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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.

Original languageEnglish
Pages (from-to)383-407
Number of pages25
JournalTheoretical Computer Science
Issue number2
StatePublished - 30 Aug 2004
Externally publishedYes


  • Chip firing games
  • Discrete dynamical models
  • Integer partitions
  • Lattices
  • Sandpile models


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