Picture of athlete cycling

Open Access research with a real impact on health...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the Physical Activity for Health Group based within the School of Psychological Sciences & Health. Research here seeks to better understand how and why physical activity improves health, gain a better understanding of the amount, intensity, and type of physical activity needed for health benefits, and evaluate the effect of interventions to promote physical activity.

Explore open research content by Physical Activity for Health...

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

[img]
Preview
Text (Dukes-Selig-ENDM2016-Decomposing-recurrent-states-of-the-abelian-sandpile-model)
Dukes_Selig_ENDM2016_Decomposing_recurrent_states_of_the_abelian_sandpile_model.pdf - Final Published Version
License: Creative Commons Attribution 4.0 logo

Download (273kB) | Preview

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.