{"paper":{"title":"The cleanness of (symbolic) 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":"Ali Soleyman Jahan, Somayeh Bandari","submitted_at":"2015-05-04T13:44:18Z","abstract_excerpt":"Let $\\Delta$ be a pure simplicial complex and $I_\\Delta$ its Stanley-Reisner ideal in a polynomial ring $S$. We show that $\\Delta$ is a matroid (complete intersection) if and only if $S/I_\\Delta^{(m)}$ ($S/I_\\Delta^m$) is clean for all $m\\in\\mathbb{N}$. If $\\dim(\\Delta)=1$, we also prove that $S/I_\\Delta^{(2)}$ ($S/I_\\Delta^2$) is clean if and only if $S/I_\\Delta^{(2)}$ ($S/I_\\Delta^2$) is Cohen-Macaulay."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00634","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"}