{"paper":{"title":"On the second powers of Stanley-Reisner ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Giancarlo Rinaldo, Ken-ichi Yoshida, Naoki Terai","submitted_at":"2012-03-09T01:25:25Z","abstract_excerpt":"In this paper, we study several properties of the second power $I_{\\Delta}^2$ of a Stanley-Reisner ideal $I_{\\Delta}$ of any dimension. As the main result, we prove that $S/I_{\\Delta}$ is Gorenstein whenever $S/I_{\\Delta}^2$ is Cohen-Macaulay over any field $K$. Moreover, we give a criterion for the second symbolic power of $I_{\\Delta}$ to satisfy $(S_2)$ and to coincide with the ordinary power, respectively. Finally, we provide new examples of Stanley-Reisner ideals whose second powers are Cohen-Macaulay."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1969","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"}