2 citations · 3 across the 4 of their papers we have counts for
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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…
Minimal Cohen-Macaulay Simplicial Complexes
Hailong Dao, Joseph Doolittle, Justin Lyle
We define and study the notion of a minimal Cohen-Macaulay simplicial complex. We prove that any Cohen-Macaulay complex is shelled over a minimal one in our sense, and we give suff…
A minimal counterexample to a strengthening of Perles' conjecture
Joseph Doolittle
In this paper, we present a minimal counterexample to a conjecture of Perles that answers a question of Haase and Ziegler. The example is a simple 4-polytope that has an induced 3-…
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…