A family of matrix-tree multijections

  title={A family of matrix-tree multijections},
  author={Alex McDonough},
  journal={Algebraic Combinatorics},
  • A. McDonough
  • Published 18 July 2020
  • Mathematics
  • Algebraic Combinatorics
. 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… 
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