English

Another proof of Wilmes' conjecture

Combinatorics 2019-12-24 v6

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.

Keywords

Cite

@article{arxiv.1306.2930,
  title  = {Another proof of Wilmes' conjecture},
  author = {Sam Hopkins},
  journal= {arXiv preprint arXiv:1306.2930},
  year   = {2019}
}

Comments

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

R2 v1 2026-06-22T00:32:56.033Z