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Structure of Stable Sand Piles Model

By Thi Ha Duong Phan and Thi Thu Huong Tran

Abstract

International audienceIn 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

Topics: Sand Piles Model, lattice, Young lattice, generating tree, [ INFO.INFO-DS ] Computer Science [cs]/Data Structures and Algorithms [cs.DS], [ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM], [ MATH.MATH-CO ] Mathematics [math]/Combinatorics [math.CO]
Publisher: DMTCS
Year: 2006
OAI identifier: oai:HAL:hal-01184697v1
Provided by: Hal-Diderot

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