Avalanche polynomials
Combinatorics
2009-05-19 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0905.2823,
title = {Avalanche polynomials},
author = {Robert Cori and Anne Micheli and Dominique Rossin},
journal= {arXiv preprint arXiv:0905.2823},
year = {2009}
}
Comments
16 pages