Abstract
We study the Abelian sandpile model on different families of graphs. We introduced the avalanche polynomial which enumerates the size of the avalanches triggered by the addition of a particle on recurrent configuration. This polynomial is calculated for several families of graphs. In the case of the complete graph,the result involves some known result on Parking functions[12, 11].
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Cori, R., Dartois, A., Rossin, D. (2004). Avalanche Polynomials of Some Families of Graphs. In: Drmota, M., Flajolet, P., Gardy, D., Gittenberger, B. (eds) Mathematics and Computer Science III. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7915-6_10
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DOI: https://doi.org/10.1007/978-3-0348-7915-6_10
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