Characterizing immutable sandpiles: a first look

DOI10.1016/j.disc.2021.112657zbMath1476.05178arXiv2006.00041OpenAlexW3204820192MaRDI QIDQ2237231

Wesley J. Engelbrecht, David L. Duncan

Publication date: 27 October 2021

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.00041

zbMATH Keywords

stabilizationdiscrete Laplacianabelian sandpile

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Graph labelling (graceful graphs, bandwidth, etc.) (05C78)

Cites Work

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• Chip-firing games on graphs
• Growth rates and explosions in sandpiles
• Strong spherical asymptotics for rotor-router aggregation and the divisible sandpile
• Spanning tree formulas and Chebyshev polynomials
• Chip-firing and the critical group of a graph
• The divisible sandpile at critical density
• Self-organized criticality
• A Combinatorial Proof of the All Minors Matrix Tree Theorem
• Self-organized critical state of sandpile automaton models
• Laplacian growth, sandpiles, and scaling limits

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