2 research outputs found
Obstructions to shellability, partitionability, and sequential Cohen-Macaulayness
For a property of simplicial complexes, a simplicial complex
is an obstruction to if itself does not satisfy
but all of its proper restrictions satisfy . In this paper, we
determine all obstructions to shellability of dimension , refining the
previous work by Wachs. As a consequence we obtain that the set of obstructions
to shellability, that to partitionability and that to sequential
Cohen-Macaulayness all coincide for dimensions . We also show that these
three sets of obstructions coincide in the class of flag complexes. These
results show that the three properties, hereditary-shellability,
hereditary-partitionability, and hereditary-sequential Cohen-Macaulayness are
equivalent for these classes