{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:5CJZKKG2QQQVYJ6LESUJA43NAT","short_pith_number":"pith:5CJZKKG2","schema_version":"1.0","canonical_sha256":"e8939528da84215c27cb24a890736d04eb0b167bac32720f9064ba7c1c5071c6","source":{"kind":"arxiv","id":"2303.09021","version":2},"attestation_state":"computed","paper":{"title":"Encoding and Enumerating Acyclic Orientations of Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Francisco Reyes, Jessica Khera, Walter Carballosa","submitted_at":"2023-03-16T01:24:27Z","abstract_excerpt":"In this work we study the acyclic orientations of graphs. We obtain an encoding of the acyclic orientations of the complete $p$-partite graph with size of its parts $n_1,n_2,\\ldots,n_p$ via a vector with $p$ symbols and length $n=n_1+n_2+\\ldots+n_p$ when the parts are fixed but not the vertices in each part. We also give a recursive way to construct all acyclic orientations of a complete multipartite graph, this construction can be done by computer easily in order $\\mathcal{O}(n)$. Furthermore, we obtain a closed formula for non-isomorphic acyclic orientations of both the complete multipartite"},"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":"2303.09021","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-03-16T01:24:27Z","cross_cats_sorted":[],"title_canon_sha256":"663271169efd1c2097070ebdec0b4be0199bc950771888d0860be4585319b5fb","abstract_canon_sha256":"3a36825ae28dacad8963f9d4c4049c86dcd69a3a5b8eabfec77542a5f0d502a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:59:22.225233Z","signature_b64":"NIkY/teio0zyxt+6lJjsnIcVIGOxiJDRJ7b6/wvzgQOhuKiakY8JWzgmJnvnTfeQt0YR6nRAWy54KWS1VEoqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8939528da84215c27cb24a890736d04eb0b167bac32720f9064ba7c1c5071c6","last_reissued_at":"2026-07-05T10:59:22.224739Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:59:22.224739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Encoding and Enumerating Acyclic Orientations of Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Francisco Reyes, Jessica Khera, Walter Carballosa","submitted_at":"2023-03-16T01:24:27Z","abstract_excerpt":"In this work we study the acyclic orientations of graphs. We obtain an encoding of the acyclic orientations of the complete $p$-partite graph with size of its parts $n_1,n_2,\\ldots,n_p$ via a vector with $p$ symbols and length $n=n_1+n_2+\\ldots+n_p$ when the parts are fixed but not the vertices in each part. We also give a recursive way to construct all acyclic orientations of a complete multipartite graph, this construction can be done by computer easily in order $\\mathcal{O}(n)$. Furthermore, we obtain a closed formula for non-isomorphic acyclic orientations of both the complete multipartite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.09021","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.09021/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2303.09021","created_at":"2026-07-05T10:59:22.224797+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.09021v2","created_at":"2026-07-05T10:59:22.224797+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.09021","created_at":"2026-07-05T10:59:22.224797+00:00"},{"alias_kind":"pith_short_12","alias_value":"5CJZKKG2QQQV","created_at":"2026-07-05T10:59:22.224797+00:00"},{"alias_kind":"pith_short_16","alias_value":"5CJZKKG2QQQVYJ6L","created_at":"2026-07-05T10:59:22.224797+00:00"},{"alias_kind":"pith_short_8","alias_value":"5CJZKKG2","created_at":"2026-07-05T10:59:22.224797+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/5CJZKKG2QQQVYJ6LESUJA43NAT","json":"https://pith.science/pith/5CJZKKG2QQQVYJ6LESUJA43NAT.json","graph_json":"https://pith.science/api/pith-number/5CJZKKG2QQQVYJ6LESUJA43NAT/graph.json","events_json":"https://pith.science/api/pith-number/5CJZKKG2QQQVYJ6LESUJA43NAT/events.json","paper":"https://pith.science/paper/5CJZKKG2"},"agent_actions":{"view_html":"https://pith.science/pith/5CJZKKG2QQQVYJ6LESUJA43NAT","download_json":"https://pith.science/pith/5CJZKKG2QQQVYJ6LESUJA43NAT.json","view_paper":"https://pith.science/paper/5CJZKKG2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.09021&json=true","fetch_graph":"https://pith.science/api/pith-number/5CJZKKG2QQQVYJ6LESUJA43NAT/graph.json","fetch_events":"https://pith.science/api/pith-number/5CJZKKG2QQQVYJ6LESUJA43NAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5CJZKKG2QQQVYJ6LESUJA43NAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5CJZKKG2QQQVYJ6LESUJA43NAT/action/storage_attestation","attest_author":"https://pith.science/pith/5CJZKKG2QQQVYJ6LESUJA43NAT/action/author_attestation","sign_citation":"https://pith.science/pith/5CJZKKG2QQQVYJ6LESUJA43NAT/action/citation_signature","submit_replication":"https://pith.science/pith/5CJZKKG2QQQVYJ6LESUJA43NAT/action/replication_record"}},"created_at":"2026-07-05T10:59:22.224797+00:00","updated_at":"2026-07-05T10:59:22.224797+00:00"}