{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:PPRDQDCZ7V74EITECH3KFOM7VL","short_pith_number":"pith:PPRDQDCZ","schema_version":"1.0","canonical_sha256":"7be2380c59fd7fc2226411f6a2b99faaebd2f088b98ff8a6f5eac61284c9fcd8","source":{"kind":"arxiv","id":"1811.06882","version":3},"attestation_state":"computed","paper":{"title":"On the Homogenized Linial Arrangement: Intersection Lattice and Genocchi Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Lazar, Michelle L. Wachs","submitted_at":"2018-11-16T15:54:14Z","abstract_excerpt":"Hetyei recently introduced a hyperplane arrangement (called the homogenized Linial arrangement) and used the finite field method of Athanasiadis to show that its number of regions is a median Genocchi number. These numbers count a class of permutations known as Dumont derangements. Here, we take a different approach, which makes direct use of Zaslavsky's formula relating the intersection lattice of this arrangement to the number of regions. We refine Hetyei's result by obtaining a combinatorial interpretation of the M\\\"obius function of this lattice in terms of variants of the Dumont permutati"},"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":"1811.06882","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-16T15:54:14Z","cross_cats_sorted":[],"title_canon_sha256":"8baaf5cae0c9cfb2162a2828c70acfaca7750643a144843f21404a380ddd1381","abstract_canon_sha256":"e8c637880700d0fe4118d090ca0c457a6bf26be6f73c84b344b13415a93368cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:29.559928Z","signature_b64":"D2r5f5x5lqcqExYFDxmPc99t50N6i3axbfKQeDBXuu0Rd3jb8WVqjR5ss2AK8IOJHnQN6SWMMu+xjIJTPhTWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7be2380c59fd7fc2226411f6a2b99faaebd2f088b98ff8a6f5eac61284c9fcd8","last_reissued_at":"2026-05-17T23:46:29.559166Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:29.559166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Homogenized Linial Arrangement: Intersection Lattice and Genocchi Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Lazar, Michelle L. Wachs","submitted_at":"2018-11-16T15:54:14Z","abstract_excerpt":"Hetyei recently introduced a hyperplane arrangement (called the homogenized Linial arrangement) and used the finite field method of Athanasiadis to show that its number of regions is a median Genocchi number. These numbers count a class of permutations known as Dumont derangements. Here, we take a different approach, which makes direct use of Zaslavsky's formula relating the intersection lattice of this arrangement to the number of regions. We refine Hetyei's result by obtaining a combinatorial interpretation of the M\\\"obius function of this lattice in terms of variants of the Dumont permutati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06882","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":"1811.06882","created_at":"2026-05-17T23:46:29.559295+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.06882v3","created_at":"2026-05-17T23:46:29.559295+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.06882","created_at":"2026-05-17T23:46:29.559295+00:00"},{"alias_kind":"pith_short_12","alias_value":"PPRDQDCZ7V74","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"PPRDQDCZ7V74EITE","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"PPRDQDCZ","created_at":"2026-05-18T12:32:46.962924+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/PPRDQDCZ7V74EITECH3KFOM7VL","json":"https://pith.science/pith/PPRDQDCZ7V74EITECH3KFOM7VL.json","graph_json":"https://pith.science/api/pith-number/PPRDQDCZ7V74EITECH3KFOM7VL/graph.json","events_json":"https://pith.science/api/pith-number/PPRDQDCZ7V74EITECH3KFOM7VL/events.json","paper":"https://pith.science/paper/PPRDQDCZ"},"agent_actions":{"view_html":"https://pith.science/pith/PPRDQDCZ7V74EITECH3KFOM7VL","download_json":"https://pith.science/pith/PPRDQDCZ7V74EITECH3KFOM7VL.json","view_paper":"https://pith.science/paper/PPRDQDCZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.06882&json=true","fetch_graph":"https://pith.science/api/pith-number/PPRDQDCZ7V74EITECH3KFOM7VL/graph.json","fetch_events":"https://pith.science/api/pith-number/PPRDQDCZ7V74EITECH3KFOM7VL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PPRDQDCZ7V74EITECH3KFOM7VL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PPRDQDCZ7V74EITECH3KFOM7VL/action/storage_attestation","attest_author":"https://pith.science/pith/PPRDQDCZ7V74EITECH3KFOM7VL/action/author_attestation","sign_citation":"https://pith.science/pith/PPRDQDCZ7V74EITECH3KFOM7VL/action/citation_signature","submit_replication":"https://pith.science/pith/PPRDQDCZ7V74EITECH3KFOM7VL/action/replication_record"}},"created_at":"2026-05-17T23:46:29.559295+00:00","updated_at":"2026-05-17T23:46:29.559295+00:00"}