{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:VY7ALQIUDVSMIXFHJR2PZXFWLE","short_pith_number":"pith:VY7ALQIU","schema_version":"1.0","canonical_sha256":"ae3e05c1141d64c45ca74c74fcdcb6593cb7660843728ce2de9e35376909a0cd","source":{"kind":"arxiv","id":"1303.2302","version":2},"attestation_state":"computed","paper":{"title":"A symmetric unimodal decomposition of the derangement polynomial of type $B$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christina Savvidou, Christos A. Athanasiadis","submitted_at":"2013-03-10T09:51:28Z","abstract_excerpt":"The derangement polynomial $d_n (x)$ for the symmetric group enumerates derangements by the number of excedances. The derangement polynomial $d^B_n(x)$ for the hyperoctahedral group is a natural type $B$ analogue. A new combinatorial formula for this polynomial is given in this paper. This formula implies that $d^B_n (x)$ decomposes as a sum of two nonnegative, symmetric and unimodal polynomials whose centers of symmetry differ by a half and thus provides a new transparent proof of its unimodality. A geometric interpretation, analogous to Stanley's interpretation of $d_n (x)$ as the local $h$-"},"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":"1303.2302","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-10T09:51:28Z","cross_cats_sorted":[],"title_canon_sha256":"237a13bb7d81cb5657402c2b132b13520320a55144aab010b04c022ab1059d7e","abstract_canon_sha256":"8a887d81c8b6230d65ada06199c525fb7ff2d96d1817e34d7ff4f9d796cbd4d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:53.174589Z","signature_b64":"W8ryqL5dP3M48l2S3YjG+yITyMsGd1fNh7gCnGxumrpm4P71H746sSmWa9Ga2FGnKd5ZGkzPCNKbto3ybjuzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae3e05c1141d64c45ca74c74fcdcb6593cb7660843728ce2de9e35376909a0cd","last_reissued_at":"2026-05-18T03:30:53.173910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:53.173910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A symmetric unimodal decomposition of the derangement polynomial of type $B$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christina Savvidou, Christos A. Athanasiadis","submitted_at":"2013-03-10T09:51:28Z","abstract_excerpt":"The derangement polynomial $d_n (x)$ for the symmetric group enumerates derangements by the number of excedances. The derangement polynomial $d^B_n(x)$ for the hyperoctahedral group is a natural type $B$ analogue. A new combinatorial formula for this polynomial is given in this paper. This formula implies that $d^B_n (x)$ decomposes as a sum of two nonnegative, symmetric and unimodal polynomials whose centers of symmetry differ by a half and thus provides a new transparent proof of its unimodality. A geometric interpretation, analogous to Stanley's interpretation of $d_n (x)$ as the local $h$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2302","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":"1303.2302","created_at":"2026-05-18T03:30:53.174021+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.2302v2","created_at":"2026-05-18T03:30:53.174021+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2302","created_at":"2026-05-18T03:30:53.174021+00:00"},{"alias_kind":"pith_short_12","alias_value":"VY7ALQIUDVSM","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VY7ALQIUDVSMIXFH","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VY7ALQIU","created_at":"2026-05-18T12:28:04.890932+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/VY7ALQIUDVSMIXFHJR2PZXFWLE","json":"https://pith.science/pith/VY7ALQIUDVSMIXFHJR2PZXFWLE.json","graph_json":"https://pith.science/api/pith-number/VY7ALQIUDVSMIXFHJR2PZXFWLE/graph.json","events_json":"https://pith.science/api/pith-number/VY7ALQIUDVSMIXFHJR2PZXFWLE/events.json","paper":"https://pith.science/paper/VY7ALQIU"},"agent_actions":{"view_html":"https://pith.science/pith/VY7ALQIUDVSMIXFHJR2PZXFWLE","download_json":"https://pith.science/pith/VY7ALQIUDVSMIXFHJR2PZXFWLE.json","view_paper":"https://pith.science/paper/VY7ALQIU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.2302&json=true","fetch_graph":"https://pith.science/api/pith-number/VY7ALQIUDVSMIXFHJR2PZXFWLE/graph.json","fetch_events":"https://pith.science/api/pith-number/VY7ALQIUDVSMIXFHJR2PZXFWLE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VY7ALQIUDVSMIXFHJR2PZXFWLE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VY7ALQIUDVSMIXFHJR2PZXFWLE/action/storage_attestation","attest_author":"https://pith.science/pith/VY7ALQIUDVSMIXFHJR2PZXFWLE/action/author_attestation","sign_citation":"https://pith.science/pith/VY7ALQIUDVSMIXFHJR2PZXFWLE/action/citation_signature","submit_replication":"https://pith.science/pith/VY7ALQIUDVSMIXFHJR2PZXFWLE/action/replication_record"}},"created_at":"2026-05-18T03:30:53.174021+00:00","updated_at":"2026-05-18T03:30:53.174021+00:00"}