Archive of posts on Jan 3, 2026
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Determining the stabilizability of the abelian sandpile model
The abelian sandpile model is a cellular automaton where each cell is a sandpile that can topple to put grains on neighboring cells when having enough grains. It is stable if none of the sandpiles can topple. A natural question to ask is whether it can become stable eventually. In this article, I will show that one can determine the stabilizibility usiung integer linear programming for the abelian sandpile model on an arbitrary finite graph.
- Categories: math
- Tags: graph theory, linear programming, long paper