Decomposing recurrent states of the abelian sandpile model

Mark Dukes, Thomas Selig

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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.
Original languageEnglish
Pages (from-to)97-102
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume54C
Early online date12 Oct 2016
DOIs
Publication statusPublished - 31 Oct 2016

Keywords

  • Abelian sandpile model
  • recurrrent states
  • graph decomposition
  • sandpile group
  • level polynomial

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