{"paper":{"title":"Stanley depth and symbolic powers 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":"2013-06-03T19:16:26Z","abstract_excerpt":"The aim of this paper is to study the Stanley depth of symbolic powers of a squarefree monomial ideal. We prove that for every squarefree monomial ideal $I$ and every pair of integers $k, s\\geq 1$, the inequalities ${\\rm sdepth} (S/I^{(ks)}) \\leq {\\rm sdepth} (S/I^{(s)})$ and ${\\rm sdepth} (I^{(ks)}) \\leq {\\rm sdepth} (I^{(s)})$ hold. If moreover $I$ is unmixed of height $d$, then we show that for every integer $k\\geq1$, ${\\rm sdepth}(I^{(k+d)})\\leq {\\rm sdepth}(I^{{(k)}})$ and ${\\rm sdepth}(S/I^{(k+d)})\\leq {\\rm sdepth}(S/I^{{(k)}})$. Finally, we consider the limit behavior of the Stanley dep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0542","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"}