  The (univariate) avalanche polynomial of a graph, introduced by Cori, Dartois
and Rossin in 2006, captures the distribution of the length of (principal)
avalanches in the abelian sandpile model. This polynomial has been used to show
that the avalanche distribution in the sandpile model on a multiple wheel graph
does not follow the expected power law function. In this article, we introduce
the (multivariate) avalanche polynomial that enumerates the toppling sequences
of all principal avalanches. This polynomial generalizes the univariate
avalanche polynomial and encodes more information. In particular, the avalanche
polynomial of a tree uniquely identifies the underlying tree. In this paper,
the avalanche polynomial is characterized for trees, cycles, wheels, and
complete graphs.
