Year: 2000
Type: preprint
Abstract: 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 SPM(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 SPM(infini), 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 the cardinal of SPM(n), where no closed formula have ever been found.
Source: arXiv (Cornell University)
Authors: Latapy, M., Mantaci, R., Morvan, M., Phan, H. D.
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394657996