Decomposing recurrent states of the abelian sandpile model

Mark Dukes; Thomas Selig

doi:10.1016/j.endm.2016.09.018

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 language	English
Pages (from-to)	97-102
Number of pages	6
Journal	Electronic Notes in Discrete Mathematics
Volume	54C
Early online date	12 Oct 2016
DOIs	https://doi.org/10.1016/j.endm.2016.09.018
Publication status	Published - 31 Oct 2016

Keywords

Abelian sandpile model
recurrrent states
graph decomposition
sandpile group
level polynomial

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title = "Decomposing recurrent states of the abelian sandpile model",

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.",

keywords = "Abelian sandpile model, recurrrent states, graph decomposition, sandpile group, level polynomial",

author = "Mark Dukes and Thomas Selig",

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T1 - Decomposing recurrent states of the abelian sandpile model

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AU - Selig, Thomas

PY - 2016/10/31

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N2 - 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.

AB - 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.

KW - Abelian sandpile model

KW - recurrrent states

KW - graph decomposition

KW - sandpile group

KW - level polynomial

UR - http://www.sciencedirect.com/science/journal/15710653

U2 - 10.1016/j.endm.2016.09.018

DO - 10.1016/j.endm.2016.09.018

M3 - Article

SN - 1571-0653

VL - 54C

SP - 97

EP - 102

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

Decomposing recurrent states of the abelian sandpile model

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New combinatorial perspectives on the abelian sandpile model

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Decomposing recurrent states of the abelian sandpile model

Abstract

Keywords

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New combinatorial perspectives on the abelian sandpile model

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