3 citations · 8 across the 12 of their papers we have counts for
16 papers
The evolution of the permutahedron
Maurício Collares, Joseph Doolittle, Joshua Erde
In their seminal paper introducing the theory of random graphs, Erdős and Rényi considered the evolution of the structure of a random subgraph of as the density increases fro…
Generalized Heawood Graphs and Triangulations of Tori
Cesar Ceballos, Joseph Doolittle
The Heawood graph is a remarkable graph that played a fundamental role in the development of the theory of graph colorings on surfaces in the 19th and 20th centuries. Based on perm…
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…
A Universal Construction for Unique Sink Orientations
Michaela Borzechowski, Joseph Doolittle, Simon Weber
Unique Sink Orientations (USOs) of cubes can be used to capture the combinatorial structure of many essential algebraic and geometric problems. For various structural and algorithm…
Subword Complexes and Kalai's Conjecture on Reconstruction of Spheres
Cesar Ceballos, Joseph Doolittle
A famous theorem in polytope theory states that the combinatorial type of a simplicial polytope is completely determined by its facet-ridge graph. This celebrated result was proven…
Common tangents to convex bodies
Federico Castillo, Joseph Doolittle, Jose Alejandro Samper
It is well-known since the time of the Greeks that two disjoint circles in the plane have four common tangent lines. Cappell et al. proved a generalization of this fact for properl…