{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MHEZOHA5O4FF2WOWBPOCKMGMYF","short_pith_number":"pith:MHEZOHA5","schema_version":"1.0","canonical_sha256":"61c9971c1d770a5d59d60bdc2530ccc16465e7d711a3d837f20c2f1a2aff616f","source":{"kind":"arxiv","id":"1301.6509","version":2},"attestation_state":"computed","paper":{"title":"On Multiple Pattern Avoiding Set Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Shattuck, Toufik Mansour, V\\'it Jel\\'inek","submitted_at":"2013-01-28T10:33:24Z","abstract_excerpt":"We study classes of set partitions determined by the avoidance of multiple patterns, applying a natural notion of partition containment that has been introduced by Sagan. We say that two sets S and T of patterns are equivalent if for each n, the number of partitions of size n avoiding all the members of S is the same as the number of those that avoid all the members of T.\n  Our goal is to classify the equivalence classes among two-element pattern sets of several general types. First, we focus on pairs of patterns {\\sigma,\\tau}, where \\sigma\\ is a pattern of size three with at least two distinc"},"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":"1301.6509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-28T10:33:24Z","cross_cats_sorted":[],"title_canon_sha256":"4c6f5478b55743bf8db53320b226201c044751b29502fa06ec91649490e17a99","abstract_canon_sha256":"d58f62731118bed43c8c85d04f01c779a29e36d28b9930d1783ec1132d4bbc3b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:13.171796Z","signature_b64":"KLBvZ88EcNuvyroyT8/aM2IjMPD7NhE5C54+znunMtYFduzPgQpmDkrhEky4hDLZxV3zm51TmVG8u88GrczzBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61c9971c1d770a5d59d60bdc2530ccc16465e7d711a3d837f20c2f1a2aff616f","last_reissued_at":"2026-05-18T03:35:13.171011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:13.171011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Multiple Pattern Avoiding Set Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mark Shattuck, Toufik Mansour, V\\'it Jel\\'inek","submitted_at":"2013-01-28T10:33:24Z","abstract_excerpt":"We study classes of set partitions determined by the avoidance of multiple patterns, applying a natural notion of partition containment that has been introduced by Sagan. We say that two sets S and T of patterns are equivalent if for each n, the number of partitions of size n avoiding all the members of S is the same as the number of those that avoid all the members of T.\n  Our goal is to classify the equivalence classes among two-element pattern sets of several general types. First, we focus on pairs of patterns {\\sigma,\\tau}, where \\sigma\\ is a pattern of size three with at least two distinc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6509","kind":"arxiv","version":2},"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":"1301.6509","created_at":"2026-05-18T03:35:13.171137+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.6509v2","created_at":"2026-05-18T03:35:13.171137+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6509","created_at":"2026-05-18T03:35:13.171137+00:00"},{"alias_kind":"pith_short_12","alias_value":"MHEZOHA5O4FF","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MHEZOHA5O4FF2WOW","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MHEZOHA5","created_at":"2026-05-18T12:27:52.871228+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/MHEZOHA5O4FF2WOWBPOCKMGMYF","json":"https://pith.science/pith/MHEZOHA5O4FF2WOWBPOCKMGMYF.json","graph_json":"https://pith.science/api/pith-number/MHEZOHA5O4FF2WOWBPOCKMGMYF/graph.json","events_json":"https://pith.science/api/pith-number/MHEZOHA5O4FF2WOWBPOCKMGMYF/events.json","paper":"https://pith.science/paper/MHEZOHA5"},"agent_actions":{"view_html":"https://pith.science/pith/MHEZOHA5O4FF2WOWBPOCKMGMYF","download_json":"https://pith.science/pith/MHEZOHA5O4FF2WOWBPOCKMGMYF.json","view_paper":"https://pith.science/paper/MHEZOHA5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.6509&json=true","fetch_graph":"https://pith.science/api/pith-number/MHEZOHA5O4FF2WOWBPOCKMGMYF/graph.json","fetch_events":"https://pith.science/api/pith-number/MHEZOHA5O4FF2WOWBPOCKMGMYF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MHEZOHA5O4FF2WOWBPOCKMGMYF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MHEZOHA5O4FF2WOWBPOCKMGMYF/action/storage_attestation","attest_author":"https://pith.science/pith/MHEZOHA5O4FF2WOWBPOCKMGMYF/action/author_attestation","sign_citation":"https://pith.science/pith/MHEZOHA5O4FF2WOWBPOCKMGMYF/action/citation_signature","submit_replication":"https://pith.science/pith/MHEZOHA5O4FF2WOWBPOCKMGMYF/action/replication_record"}},"created_at":"2026-05-18T03:35:13.171137+00:00","updated_at":"2026-05-18T03:35:13.171137+00:00"}