3 citations · 8 across the 12 of their papers we have counts for
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math.CO2017★ 1 cited
Higher Nerves of Simplicial Complexes
Hailong Dao, Joseph Doolittle, Ken Duna +3
We investigate generalized notions of the nerve complex for the facets of a simplicial complex. We show that the homologies of these higher nerve complexes determine the depth of t…
math.CO2017★ 2 cited
Reconstructing Nearly Simple Polytopes from their Graph
Joseph Doolittle
We present a partial description of which polytopes are reconstructible from their graphs. This is an extension of work by Blind and Mani (1987) and Kalai (1988), which showed that…
math.CO2017
On the reconstruction of polytopes
Joseph Doolittle, Eran Nevo, Guillermo Pineda-Villavicencio +2
Blind and Mani, and later Kalai, showed that the face lattice of a simple polytope is determined by its graph, namely its -skeleton. Call a vertex of a -polytope \emph{nonsim…