Algebraic and combinatorial aspects of sandpile monoids on directed graphs

Understand

The sandpile group of a graph is a well-studied object that combines ideas from algebraic graph theory, group theory, dynamical systems, and statistical physics.

• A graph's sandpile group is part of a larger algebraic structure on the graph, known as its sandpile monoid.
• Most of the work on sandpiles so far has focused on the sandpile group rather than the sandpile monoid of a graph, and has also assumed the underlying graph to be undirected.
• A notable exception is the recent work of Babai and Toumpakari, which builds up the theory of sandpile monoids on directed graphs from scratch and provides many connections between the combinatorics of a graph and the algebraic aspects of its sandpile monoid.