  In this paper, we study the dynamics of sand grains falling in sand piles.
Usually sand piles are characterized by a decreasing integer partition and
grain moves are described in terms of transitions between such partitions. We
study here four main transition rules. The more classical one, introduced by
Brylawski (1973) induces a lattice structure $L_B (n)$ (called dominance
ordering) between decreasing partitions of a given integer n. We prove that a
more restrictive transition rule, called SPM rule, induces a natural partition
of L_B (n) in suborders, each one associated to a fixed point for SPM rule. In
the second part, we extend the SPM rule in a natural way and obtain a model
called Chip Firing Game (Goles and Kiwi, 1993). We prove that this new model
has interesting properties: the induced order is a lattice, a natural greedoid
can be associated to the model and it also defines a strongly convergent game.
In the last section, we generalize the SPM rule in another way and obtain other
lattice structure parametrized by some t: L(n,t), which form for -n+2 <= t <= n
a decreasing sequence of lattices. For each t, we characterize the fixed point
of L(n,t) and give the value of its maximal sized chain's lenght. We also note
that L(n,-n+2) is the lattice of all compositions of n.
