{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:L5S3Y7MMDIEDJ7RBDM5ZVO23TI","short_pith_number":"pith:L5S3Y7MM","schema_version":"1.0","canonical_sha256":"5f65bc7d8c1a0834fe211b3b9abb5b9a2fd5a43b0633a1cdf29f8a474fa98764","source":{"kind":"arxiv","id":"1908.05014","version":1},"attestation_state":"computed","paper":{"title":"A Combinatorial Analysis Of Higher Order Generalised Geometric Polynomials: A Generalisation Of Barred Preferential Arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Be\\'ata B\\'enyi, Cristina B. Corcino, Roberto B. Corcino, Sithembele Nkonkobe","submitted_at":"2019-08-14T08:32:39Z","abstract_excerpt":"A barred preferential arrangement is a preferential arrangement, onto which in-between the blocks of the preferential arrangement a number of identical bars are inserted. We offer a generalisation of barred preferential arrangements by making use of the generalised Stirling numbers proposed by Hsu and Shiue (1998). We discuss how these generalised barred preferential arrangements offer a unified combinatorial interpretation of geometric polynomials. We also discuss asymptotic properties of these numbers."},"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":"1908.05014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-14T08:32:39Z","cross_cats_sorted":[],"title_canon_sha256":"969e1297ebb12fbfac76e5f3b32f63dc0d08c4f4aa4b6711a4007c63b0595154","abstract_canon_sha256":"18d662af7e20accbed1cffd1b9f94e0fa8db2108dd3c5ec24645947bcf4ad8d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:55:59.142219Z","signature_b64":"YTUXX0cCuNgMXerV+niPe+YSIurqlofuSAMDLP9i92wLUo9u3F9t/ZRY/EpK906unimGGwmmDZhPfOJ+A1BSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f65bc7d8c1a0834fe211b3b9abb5b9a2fd5a43b0633a1cdf29f8a474fa98764","last_reissued_at":"2026-07-04T23:55:59.141848Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:55:59.141848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Combinatorial Analysis Of Higher Order Generalised Geometric Polynomials: A Generalisation Of Barred Preferential Arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Be\\'ata B\\'enyi, Cristina B. Corcino, Roberto B. Corcino, Sithembele Nkonkobe","submitted_at":"2019-08-14T08:32:39Z","abstract_excerpt":"A barred preferential arrangement is a preferential arrangement, onto which in-between the blocks of the preferential arrangement a number of identical bars are inserted. We offer a generalisation of barred preferential arrangements by making use of the generalised Stirling numbers proposed by Hsu and Shiue (1998). We discuss how these generalised barred preferential arrangements offer a unified combinatorial interpretation of geometric polynomials. We also discuss asymptotic properties of these numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05014","kind":"arxiv","version":1},"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/1908.05014/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":"1908.05014","created_at":"2026-07-04T23:55:59.141904+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.05014v1","created_at":"2026-07-04T23:55:59.141904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05014","created_at":"2026-07-04T23:55:59.141904+00:00"},{"alias_kind":"pith_short_12","alias_value":"L5S3Y7MMDIED","created_at":"2026-07-04T23:55:59.141904+00:00"},{"alias_kind":"pith_short_16","alias_value":"L5S3Y7MMDIEDJ7RB","created_at":"2026-07-04T23:55:59.141904+00:00"},{"alias_kind":"pith_short_8","alias_value":"L5S3Y7MM","created_at":"2026-07-04T23:55:59.141904+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/L5S3Y7MMDIEDJ7RBDM5ZVO23TI","json":"https://pith.science/pith/L5S3Y7MMDIEDJ7RBDM5ZVO23TI.json","graph_json":"https://pith.science/api/pith-number/L5S3Y7MMDIEDJ7RBDM5ZVO23TI/graph.json","events_json":"https://pith.science/api/pith-number/L5S3Y7MMDIEDJ7RBDM5ZVO23TI/events.json","paper":"https://pith.science/paper/L5S3Y7MM"},"agent_actions":{"view_html":"https://pith.science/pith/L5S3Y7MMDIEDJ7RBDM5ZVO23TI","download_json":"https://pith.science/pith/L5S3Y7MMDIEDJ7RBDM5ZVO23TI.json","view_paper":"https://pith.science/paper/L5S3Y7MM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.05014&json=true","fetch_graph":"https://pith.science/api/pith-number/L5S3Y7MMDIEDJ7RBDM5ZVO23TI/graph.json","fetch_events":"https://pith.science/api/pith-number/L5S3Y7MMDIEDJ7RBDM5ZVO23TI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L5S3Y7MMDIEDJ7RBDM5ZVO23TI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L5S3Y7MMDIEDJ7RBDM5ZVO23TI/action/storage_attestation","attest_author":"https://pith.science/pith/L5S3Y7MMDIEDJ7RBDM5ZVO23TI/action/author_attestation","sign_citation":"https://pith.science/pith/L5S3Y7MMDIEDJ7RBDM5ZVO23TI/action/citation_signature","submit_replication":"https://pith.science/pith/L5S3Y7MMDIEDJ7RBDM5ZVO23TI/action/replication_record"}},"created_at":"2026-07-04T23:55:59.141904+00:00","updated_at":"2026-07-04T23:55:59.141904+00:00"}