Decomposing recurrent states of the abelian sandpile model
Dukes, Mark and Selig, Thomas (2016) Decomposing recurrent states of the abelian sandpile model. Electronic Notes in Discrete Mathematics, 54C. pp. 97-102. ISSN 1571-0653 (https://doi.org/10.1016/j.endm.2016.09.018)
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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.
ORCID iDs
Dukes, Mark ORCID: https://orcid.org/0000-0002-2779-2680 and Selig, Thomas ORCID: https://orcid.org/0000-0002-2736-4416;-
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Item type: Article ID code: 58012 Dates: DateEvent31 October 2016Published12 October 2016Published Online29 April 2016AcceptedSubjects: Science > Mathematics Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 03 Oct 2016 13:23 Last modified: 24 Oct 2024 00:28 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/58012