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We show that $S/I$ is pretty clean if either: 1) $u_1,u_2,..., u_t$ is a filter-regular sequence, 2) $u_1,u_2,..., u_t$ is a $d$-sequence; or 3) $I$ is almost complete intersection. In particular, in each of these cases, $S/I$ is sequentially Cohen-Macaulay and both Stanley's and $h$-regularity conjectures, on Stanley decompositions, hold for $S/I$. Also, we prove that if $I$ is the Stanley-Reisner ideal of a locally complete intersection simplicial complex on $[n]$"},"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":"1112.5159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-21T20:59:49Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ed6e811eaf07bf0a9c5ad111127da641ccd715171c90a55ecdde7f94b4c194db","abstract_canon_sha256":"45fc92705a4f1c451b348f75dbfcf192b439e3e58bd1a39765047f960628d744"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:50.138364Z","signature_b64":"kv08e61sDO6ay9BY4Q7Q0uHLtx4rulfHQSymbHYdGTjyGGZyiAEcqGnfsFY9brCj4BRciWxkr1UvjvYZ7b8oCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a66fe811c3912450ce412c300f5f22ca106b339cf617193412c06e220a63a93","last_reissued_at":"2026-05-18T03:04:50.137644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:50.137644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Filter-regular sequences, almost complete intersections and Stanley's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Ali Soleyman Jahan, Kamran Divaani-Aazar, Somayeh Bandari","submitted_at":"2011-12-21T20:59:49Z","abstract_excerpt":"Let $K$ be a field and $I$ a monomial ideal of the polynomial ring $S=K[x_1,..., x_n]$ generated by monomials $u_1,u_2,..., u_t$. 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