Playing with Abelian Sandpiles

Imagine yourself on a beach, playing in the sand. You begin to make a sandpile by adding handfuls of sand. Now you consider dropping another grain of sand onto the pile but you don’t know what will happen. It may cause nothing to happen or it may cause the entire pile to collapse in a massive avalanche. This is the idea behind the Abelian sandpile model. We measure the sizes of these avalanches and build what is called the avalanche polynomial. This topic is based on graph theory and enumerative combinatorics.