{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V7HH6CFUYNQCGZFHLQ27ZKH2EN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c270fb3fd9a6eec2ce2cb14baa449c971943c703237784f8a6d28e785c834312","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-24T15:20:13Z","title_canon_sha256":"caafc2b14766bff3d4b63adeb9cd016c0ec0bda00d497d21ba292901e231afb1"},"schema_version":"1.0","source":{"id":"1711.09016","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09016","created_at":"2026-05-18T00:29:24Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09016v2","created_at":"2026-05-18T00:29:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09016","created_at":"2026-05-18T00:29:24Z"},{"alias_kind":"pith_short_12","alias_value":"V7HH6CFUYNQC","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V7HH6CFUYNQCGZFH","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V7HH6CFU","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:7667bceea7efdf300a010e758788f4c170661ca41f8f2cadc6caf36309648799","target":"graph","created_at":"2026-05-18T00:29:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Binomial-Eulerian polynomials were introduced by Postnikov, Reiner and Williams. In this paper, properties of the binomial-Eulerian polynomials, including recurrence relations and generating functions are studied. We present three constructive proofs of the recurrence relations for binomial-Eulerian polynomials. Moreover, we give a combinatorial interpretation of the Betti number of the complement of the k-equal real hyperplane arrangement.","authors_text":"Jun Ma, Shi-Mei Ma, Yeong-Nan Yeh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-24T15:20:13Z","title":"Recurrence relations for binomial-Eulerian polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09016","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bbfec30169de74d542aa5413f33b96dcb1a76737270d198f94bccda9c765845c","target":"record","created_at":"2026-05-18T00:29:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c270fb3fd9a6eec2ce2cb14baa449c971943c703237784f8a6d28e785c834312","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-24T15:20:13Z","title_canon_sha256":"caafc2b14766bff3d4b63adeb9cd016c0ec0bda00d497d21ba292901e231afb1"},"schema_version":"1.0","source":{"id":"1711.09016","kind":"arxiv","version":2}},"canonical_sha256":"afce7f08b4c3602364a75c35fca8fa234f7961461fc0ae9098fb57ac3480518b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afce7f08b4c3602364a75c35fca8fa234f7961461fc0ae9098fb57ac3480518b","first_computed_at":"2026-05-18T00:29:24.013670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:24.013670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e44IU7PIlA3SNpaebKByYaxnvhr9wApnIJmmdhRxY/tx96vXPovtzvO66fgAUbXtxFQhi9PjroTjiN5yffFUDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:24.014229Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.09016","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbfec30169de74d542aa5413f33b96dcb1a76737270d198f94bccda9c765845c","sha256:7667bceea7efdf300a010e758788f4c170661ca41f8f2cadc6caf36309648799"],"state_sha256":"1049ef02a280d37a9b5a6855c74d9da923dcb2eda0a1b0f6fabbcc4a1a790a03"}