{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:BBIXOPIEK3DMXUX27Z3KRXY7PB","short_pith_number":"pith:BBIXOPIE","schema_version":"1.0","canonical_sha256":"0851773d0456c6cbd2fafe76a8df1f784d941ffce2e7a6ab4addb01f10a66cc6","source":{"kind":"arxiv","id":"1301.6779","version":3},"attestation_state":"computed","paper":{"title":"Results on the regularity of square-free monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Huy T\\`ai H\\`a, Russ Woodroofe","submitted_at":"2013-01-28T21:26:59Z","abstract_excerpt":"In a 2008 paper, the first author and Van Tuyl proved that the regularity of the edge ideal of a graph G is at most one greater than the matching number of G. In this note, we provide a generalization of this result to any square-free monomial ideal. We define a 2-collage in a simple hypergraph to be a collection of edges with the property that for any edge E of the hypergraph, there exists an edge F in the collage such that |E \\ F| < 2. The Castelnuovo-Mumford regularity of the edge ideal of a simple hypergraph is bounded above by a multiple of the minimum size of a 2-collage. We also give a "},"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":"1301.6779","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-28T21:26:59Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"c094d313fdf2dbeabd949d4de6006836acd2dd13807292747eece05d37e2a354","abstract_canon_sha256":"685eadcc11bfa1cd98c1d382225a8c242e359801e43f8b4e4219de15701f67f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:42.631114Z","signature_b64":"OZL4cPHhPi2mWdgUcGnEPK2nC1lOpqyZLvAM7gl2vEEwv4DaQn8T+qJXEnVee3v6Deow6x0ac9R1M0hbyLxACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0851773d0456c6cbd2fafe76a8df1f784d941ffce2e7a6ab4addb01f10a66cc6","last_reissued_at":"2026-05-18T00:58:42.630572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:42.630572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Results on the regularity of square-free monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Huy T\\`ai H\\`a, Russ Woodroofe","submitted_at":"2013-01-28T21:26:59Z","abstract_excerpt":"In a 2008 paper, the first author and Van Tuyl proved that the regularity of the edge ideal of a graph G is at most one greater than the matching number of G. In this note, we provide a generalization of this result to any square-free monomial ideal. We define a 2-collage in a simple hypergraph to be a collection of edges with the property that for any edge E of the hypergraph, there exists an edge F in the collage such that |E \\ F| < 2. The Castelnuovo-Mumford regularity of the edge ideal of a simple hypergraph is bounded above by a multiple of the minimum size of a 2-collage. We also give a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6779","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.6779","created_at":"2026-05-18T00:58:42.630646+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.6779v3","created_at":"2026-05-18T00:58:42.630646+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6779","created_at":"2026-05-18T00:58:42.630646+00:00"},{"alias_kind":"pith_short_12","alias_value":"BBIXOPIEK3DM","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"BBIXOPIEK3DMXUX2","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"BBIXOPIE","created_at":"2026-05-18T12:27:38.830355+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BBIXOPIEK3DMXUX27Z3KRXY7PB","json":"https://pith.science/pith/BBIXOPIEK3DMXUX27Z3KRXY7PB.json","graph_json":"https://pith.science/api/pith-number/BBIXOPIEK3DMXUX27Z3KRXY7PB/graph.json","events_json":"https://pith.science/api/pith-number/BBIXOPIEK3DMXUX27Z3KRXY7PB/events.json","paper":"https://pith.science/paper/BBIXOPIE"},"agent_actions":{"view_html":"https://pith.science/pith/BBIXOPIEK3DMXUX27Z3KRXY7PB","download_json":"https://pith.science/pith/BBIXOPIEK3DMXUX27Z3KRXY7PB.json","view_paper":"https://pith.science/paper/BBIXOPIE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.6779&json=true","fetch_graph":"https://pith.science/api/pith-number/BBIXOPIEK3DMXUX27Z3KRXY7PB/graph.json","fetch_events":"https://pith.science/api/pith-number/BBIXOPIEK3DMXUX27Z3KRXY7PB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BBIXOPIEK3DMXUX27Z3KRXY7PB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BBIXOPIEK3DMXUX27Z3KRXY7PB/action/storage_attestation","attest_author":"https://pith.science/pith/BBIXOPIEK3DMXUX27Z3KRXY7PB/action/author_attestation","sign_citation":"https://pith.science/pith/BBIXOPIEK3DMXUX27Z3KRXY7PB/action/citation_signature","submit_replication":"https://pith.science/pith/BBIXOPIEK3DMXUX27Z3KRXY7PB/action/replication_record"}},"created_at":"2026-05-18T00:58:42.630646+00:00","updated_at":"2026-05-18T00:58:42.630646+00:00"}