Wilmes' Conjecture and Boundary Divisors

Abstract

This paper is concerned with Wilmes' conjecture regarding abelian sandpile models. We introduce the concept of boundary divisors and use this to prove the conjecture for the first Betti number. Further results suggest that this method could be used to tackle the general case of the problem.

23 pages, 11 figures

References in corpus (2)

• Minimal Free Resolutions of the $G$-parking Function Ideal and the Toppling Ideal
• Orientations, lattice polytopes, and group arrangements I: Chromatic and tension polynomials of graphs

Cited by in corpus (1)

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