172 citations · 377 across the 33 of their papers we have counts for
5 papers · 1 filter
Homological percolation on a torus: plaquettes and permutohedra
Paul Duncan, Matthew Kahle, Benjamin Schweinhart
We study higher-dimensional homological analogues of bond percolation on a square lattice and site percolation on a triangular lattice. By taking a quotient of certain infinite cel…
Homology of configuration spaces of hard squares in a rectangle
Hannah Alpert, Ulrich Bauer, Matthew Kahle +2
We study ordered configuration spaces of hard squares in a rectangle, a generalization of the well-known "15 Puzzle". Our main interest is in the topolo…
Topology and geometry of random 2-dimensional hypertrees
Matthew Kahle, Andrew Newman
A hypertree, or -acyclic complex, is a higher-dimensional analogue of a tree. We study random -dimensional hypertrees according to the determinantal measure suggeste…
A square-grid coloring problem
Matthew Kahle, Francisco Martinez-Figueroa, Alexander Soifer
Suppose that , and we wish to plant different types of trees in the squares of an square grid. We can have as many of each type as we want. The only rule…
Topology of random 2-dimensional cubical complexes
Matthew Kahle, Elliot Paquette, Érika Roldán
We study a natural model of random 2-dimensional cubical complex which is a subcomplex of an n-dimensional cube, and where every possible square -face is included independently…