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Structure of Stable Sand Piles Model

Abstract : In this paper we study a variant of the Sand Piles Model, where the evolution rule consists of the falling down of one grain to a random column and an avalanche to reach a stable configuration. We prove that the infinite set of all stable configurations have a lattice structure which is a sublattice of Young lattice. At the end, based on a discussion about avalanches, we construct a generating tree of this model and show its strongtly recursive structure.
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Thi Ha Duong Phan, Thi Thu Huong Tran. Structure of Stable Sand Piles Model. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.407-410, ⟨10.46298/dmtcs.3493⟩. ⟨hal-01184697⟩

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