{"paper":{"title":"Depth of some square free monomial ideals","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrei Zarojanu, Dorin Popescu","submitted_at":"2012-11-05T12:24:05Z","abstract_excerpt":"Let $I\\supsetneq J$ be two square free monomial ideals of a polynomial algebra over a field generated in degree $\\geq 1$, resp. $\\geq 2$ . Almost always when $I$ contains precisely one variable, the other generators having degrees $\\geq 2$, if the Stanley depth of $I/J$ is $\\leq 2$ then the usual depth of $I/J$ is $\\leq 2$ too, that is the Stanley Conjecture holds in these cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0842","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"}