{"paper":{"title":"Stanley depth of the integral closure of monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"S. A. Seyed Fakhari","submitted_at":"2012-05-31T12:28:02Z","abstract_excerpt":"Let $I$ be a monomial ideal in the polynomial ring $S=\\mathbb{K}[x_1,...,x_n]$. We study the Stanley depth of the integral closure $\\bar{I}$ of $I$. We prove that for every integer $k\\geq 1$, the inequalities ${\\rm sdepth} (S/\\bar{I^k}) \\leq {\\rm sdepth} (S/\\bar{I})$ and ${\\rm sdepth} (\\bar{I^k}) \\leq {\\rm sdepth} (\\bar{I})$ hold. We also prove that for every monomial ideal $I\\subset S$ there exist integers $k_1,k_2\\geq 1$, such that for every $s\\geq 1$, the inequalities ${\\rm sdepth} (S/I^{sk_1}) \\leq {\\rm sdepth} (S/\\bar{I})$ and ${\\rm sdepth} (I^{sk_2}) \\leq {\\rm sdepth} (\\bar{I})$ hold. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6971","kind":"arxiv","version":3},"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"}