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The evolution of the permutahedron
MaurÃcio Collares, Joseph Doolittle, Joshua Erde
In their seminal paper introducing the theory of random graphs, ErdÅs and Rényi considered the evolution of the structure of a random subgraph of as the density increases f…
Empty simplices of large width
Joseph Doolittle, Lukas Katthän, Benjamin Nill +1
An empty simplex is a lattice simplex in which vertices are the only lattice points. We show two constructions leading to the first known empty simplices of width larger than their…
Fragmenting any Parallelepiped into a Signed Tiling
Joseph Doolittle, Alex McDonough
It is broadly known that any parallelepiped tiles space by translating copies of itself along its edges. In earlier work relating to higher-dimensional sandpile groups, the second…