Another proof of Wilmes' conjecture
arXiv:1306.2930 · doi:10.1016/j.disc.2014.01.010
Abstract
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.
8 pages, 1 figure. v2: added reference to a recent preprint of Mohammadi and Shokrieh. v3: to appear in Discrete Math, v4,v5,v6: minor typos corrected