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spm (Sand Pile Model) is a simple discrete dynamical system used in physics to represent granular objects. It is deeply related to integer partitions, and many other combinatorics problems, such as tilings or rewriting systems. The evolution of the system started with n stacked grains generates a lattice, denoted by SP M (n). We study here the structure of this lattice. We first explain how it can be constructed, by showing its strong self-similarity property. Then, we define SP M (∞), a natural extension of spm when one starts with an infinite number of grains. Again, we give an efficient construction algorithm and a coding of this lattice using a self-similar tree. The two approaches give different recursive formulae for |SP M (n)|.

International audience Eulerian numbers (and ''Alternate Eulerian numbers'') are often interpreted as distributions of statistics defined over the Symmetric group. The main purpose of this paper is to define a way to represent permutations that provides some other combinatorial interpretations of these numbers. This representation uses a one-to-one correspondence between permutations and the so-called \emphsubexceedant functions.

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