Minimal Free Resolutions of the $G$-parking Function Ideal and the Toppling Ideal

Madhusudan Manjunath, Frank-Olaf Schreyer, John Wilmes

The $G$-parking function ideal $M_G$ of a directed multigraph $G$ is a monomial ideal which encodes some of the combinatorial information of $G$. It is an initial ideal of the topp…