# A family of matrix-tree multijections

@article{McDonough2020AFO, title={A family of matrix-tree multijections}, author={Alex McDonough}, journal={Algebraic Combinatorics}, year={2020} }

. For a natural class of r × n integer matrices, we construct a non-convex polytope which periodically tiles R n . From this tiling, we provide a family of geometrically meaningful maps from a generalized sandpile group to a set of generalized spanning trees which give multijective proofs for several higher-dimensional matrix-tree theorems. In particular, these multijections can be ap- plied to graphs, regular matroids, cell complexes with a torsion-free spanning forest, and representable…

## One Citation

### Standard monomials of 1-skeleton ideals of graphs and generalized signless Laplacians

- MathematicsLinear Algebra and its Applications
- 2022

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