{"paper":{"title":"On the facet ideal of an expanded simplicial complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Rahim Rahmati-Asghar, Somayeh Moradi","submitted_at":"2017-01-17T15:45:22Z","abstract_excerpt":"For a simplicial complex $\\Delta$, the affect of the expansion functor on combinatorial properties of $\\Delta$ and algebraic properties of its Stanley-Reisner ring has been studied in some previous papers. In this paper, we consider the facet ideal $I(\\Delta)$ and its Alexander dual which we denote by $J_{\\Delta}$ to see how the expansion functor alter the algebraic properties of these ideals. It is shown that for any expansion $\\Delta^{\\alpha}$ the ideals $J_{\\Delta}$ and $J_{\\Delta^{\\alpha}}$ have the same total Betti numbers and their Cohen-Macaulayness are equivalent, which implies that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04734","kind":"arxiv","version":1},"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"}