Sandpiles and order structure of integer partitions

Eric Goles, Michel Morvan, Ha Duong Phan

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


In this paper, we study the orders obtained by the generalized dynamics of the sand piles model (SPM). We show that these orders are suborders of L B, lattice of integer partitions introduced in Brylawski (Discrete Math. 6 (1973) 201), and we deduce from that a characterization of their fixed point. We prove that these orders form an increasing sequence of lattices from SPM to L B. We then characterize longest paths in these lattices and give a formula describing their length.

Original languageEnglish
Pages (from-to)51-64
Number of pages14
JournalDiscrete Applied Mathematics
Issue number1-3
StatePublished - 15 Mar 2002
Externally publishedYes


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