Description
- 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. There are extensions of the matrix-tree theorem which express the size of a generalized sandpile group as a weighted count of generalized spanning trees. In this manuscript, we elevate this enumerative relationship to a combinatorial relationship by constructing a family of many-to-one maps, which we call multijections. This construction is geometric and involves a periodic tiling of n-space made up of non-convex polyhedra.
- Notes:
- Thesis (Ph. D.)--Brown University, 2021
Citation
McDonough, Alex,
"Higher-Dimensional Sandpile Groups and Matrix-Tree Multijections"
(2021).
Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:q5qpgrqx/
