A Higher-Dimensional Sandpile Map

Abstract: Traditionally, the sandpile group is defined on a graph and the Matrix-Tree Theorem says that this group's size is equal to the number of spanning trees. An extension of the Matrix-Tree Theorem gives a relationship between the sandpile group and bases of a class of orientable arithmetic matroids. I provide a family of combinatorially meaningful maps between these two sets. This generalizes a bijection given by Backman, Baker, and Yuen and extends work by Duval, Klivans, and Martin. I will not assume any background beyond undergraduate linear algebra.

combinatorics

Audience: researchers in the topic

York University Applied Algebra Seminar