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Discrete Mathematics & Theoretical Computer Science |
Thi Ha Duong Phan ; Thi Thu Huong Tran - Structure of Stable Sand Piles Model
dmtcs:3493 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities - https://doi.org/10.46298/dmtcs.3493Structure of Stable Sand Piles ModelArticle
Authors: Thi Ha Duong Phan 1; Thi Thu Huong Tran 
2
- 1 Laboratoire d'informatique Algorithmique : Fondements et Applications
- 2 Institut de Mathématiques [Hanoi]
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.
Source: HAL:hal-01184697v1
Volume: DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities
Section: Proceedings
Published on: January 1, 2006
Imported on: May 10, 2017
Keywords: 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]
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