  We present a new proof of the monomial case of Wilmes' conjecture, which
gives a formula for the coarsely-graded Betti numbers of the G-parking function
ideal in terms of maximal parking functions of contractions of G. Our proof is
via poset topology and relies on a theorem of Gasharov, Peeva, and Welker that
connects the Betti numbers of a monomial ideal to the topology of its
lcm-lattice.

Combinatorics