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It is shown that $S/I(c_d(\\mathcal{C}))$ satisfies Stanley's conjecture, where $I(c_d(\\mathcal{C}))$ is the edge ideal of the $d$-complement of $\\mathcal{C}$. This, in particular shows that $S/I$ satisfies Stanley's conjecture, where $I$ is a quadratic monomial ideal with linear resolution. We also define the notion of Sch"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.5270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-09-18T11:45:42Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c58ec106bca1eebcb36ee8ab6718780e3101bb3f31a7fb3faf017ed5ade88398","abstract_canon_sha256":"9f9e17cbe112900f6459846eda250493c835ed71d2fc44cff063a44a080c2b17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:30.114616Z","signature_b64":"xIEhzg/KNsWbNBED9XVTaZdtKVy71HPN+x6+C5RgulOYLwyatOeQgUS0oppu/oQV/BlIaPYkQT+iIXv0dsYZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ed93cef1c46f30ef468cc71f4e351ce9c29e2bd57972bb9d0035ba85f28f1f8","last_reissued_at":"2026-05-18T02:42:30.113920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:30.113920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Stanley depth of squarefree 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":"2014-09-18T11:45:42Z","abstract_excerpt":"Let $\\mathbb{K}$ be a field and $S=\\mathbb{K}[x_1,\\dots,x_n]$ be the polynomial ring in $n$ variables over the field $\\mathbb{K}$. Suppose that $\\mathcal{C}$ is a chordal clutter with $n$ vertices and assume that the minimum edge cardinality of $\\mathcal{C}$ is at least $d$. It is shown that $S/I(c_d(\\mathcal{C}))$ satisfies Stanley's conjecture, where $I(c_d(\\mathcal{C}))$ is the edge ideal of the $d$-complement of $\\mathcal{C}$. This, in particular shows that $S/I$ satisfies Stanley's conjecture, where $I$ is a quadratic monomial ideal with linear resolution. 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