{"paper":{"title":"Obstructions to shellability, partitionability, and sequential Cohen-Macaulayness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kenji Kashiwabara, Masahiro Hachimori","submitted_at":"2010-03-10T07:55:46Z","abstract_excerpt":"For a property $\\cal P$ of simplicial complexes, a simplicial complex $\\Gamma$ is an obstruction to $\\cal P$ if $\\Gamma$ itself does not satisfy $\\cal P$ but all of its proper restrictions satisfy $\\cal P$. In this paper, we determine all obstructions to shellability of dimension $\\le 2$, 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 $\\le 2$. We also show that these three sets of obstructions coincide in the class of flag complexes. Thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2037","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}