2009/05/18 by Robert Cori, Cori, Robert, Anne Micheli +3
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.0905.2823
openalex publication_date 2009/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The avalanche polynomial on a graph captures the distribution of avalanches in the abelian sandpile model. Studied on trees, this polynomial could be defined by simply considering the size of the subtrees of the original tree. In this article, we study some properties of this polynomial on plane trees. Previously it has been proved that two different trees could have the same avalanche polynomial. We show here that the problem of finding a tree with a prescribed polynomial is NP-complete. In a second part, we study the average and the variance of the avalanche distribution on trees and give a closed formula.