Unexpected systems of parameters for contractible or acyclic complexes

Ascertain whether a d-dimensional contractible (or acyclic) simplicial complex Δ can admit an unexpected system of parameters as defined in Definition 3.1.

Background

Most existence results in the paper concern homology spheres, where Macaulay duality yields a single dual generator. For non–homology spheres, establishing unexpected sops appears to require new techniques.

Motivated by the nonexistence results for collapsible complexes in certain degrees and by the structural differences for non–homology spheres, the authors explicitly raise the question for contractible or acyclic complexes.