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math.CO2018
Resolving Stanley's conjecture on -fold acyclic complexes
Joseph Doolittle, Bennet Goeckner
In 1993 Stanley showed that if a simplicial complex is acyclic over some field, then its face poset can be decomposed into disjoint rank boolean intervals whose minimal faces t…
math.CO2018
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-…