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Our main results extend Abedelfatah's recent work on the Eisenbud-Green-Harris conjecture, Shakin's generalization of Macaulay and Bigatti-Hulett-Pardue theorems on Betti numbers and, when char(K)=0, Mermin-Murai theorem on the Lex-Plus-Power inequality, from monomial regular sequences to a larger class of ideal"},"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":"1308.4659","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-08-21T18:58:34Z","cross_cats_sorted":[],"title_canon_sha256":"793f315359511c23ec764f2805021bc8098c5deb8a700976caafbd049b652b98","abstract_canon_sha256":"76429c9fb1f53602d45b9d169d2a0a8e88000542ef40587349f0d4ef38eea2f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:21.363003Z","signature_b64":"LgPSydKJvDUYYbW3VWP9d01CzEiQixgAONHNwJvrGnFaFsmVVETwCoSTDf00dtjg+vXDG8Qt1c4r2zjzpERGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fbec4889fe689a11cfae554f5e8706e5fa1aa21d959540dfd53b7d6db2b9b3d","last_reissued_at":"2026-05-18T03:15:21.362417Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:21.362417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distractions of Shakin rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Enrico Sbarra, Giulio Caviglia","submitted_at":"2013-08-21T18:58:34Z","abstract_excerpt":"We study, by means of embeddings of Hilbert functions, a class of rings which we call Shakin rings, i.e. quotients K[X_1,...,X_n]/a of a polynomial ring over a field K by ideals a=L+P which are the sum of a piecewise lex-segment ideal L, as defined by Shakin, and a pure powers ideal P. 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