Abstract
The recurrent states of the Abelian sandpile model (ASM) are those states that appear infinitely often. For this reason they occupy a central position in ASM research. We present several new results for classifying recurrent states of the Abelian sandpile model on graphs that may be decomposed in a variety of ways. These results allow us to classify, for certain families of graphs, recurrent states in terms of the recurrent states of its components. We use these decompositions to give recurrence relations for the generating functions of the level statistic on the recurrent configurations. We also interpret our results with respect to the sandpile group.
Original language | English |
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Pages (from-to) | 97-102 |
Number of pages | 6 |
Journal | Electronic Notes in Discrete Mathematics |
Volume | 54 |
DOIs | |
Publication status | Published - 1 Oct 2016 |
Externally published | Yes |
Keywords
- Abelian sandpile model
- graph decomposition
- level polynomial
- recurrent states
- sandpile group