{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2V4U3GDYRMVORVORWTMA326TLG","short_pith_number":"pith:2V4U3GDY","schema_version":"1.0","canonical_sha256":"d5794d98788b2ae8d5d1b4d80debd359988d370c02a3b4b2c69f8182fedf5277","source":{"kind":"arxiv","id":"1401.6273","version":1},"attestation_state":"computed","paper":{"title":"Mutual Interlacing and Eulerian-like Polynomials for Weyl Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Arthur L.B. Yang, Philip B. Zhang","submitted_at":"2014-01-24T07:33:10Z","abstract_excerpt":"We use the method of mutual interlacing to prove two conjectures on the real-rootedness of Eulerian-like polynomials: Brenti's conjecture on $q$-Eulerian polynomials for Weyl groups of type $D$, and Dilks, Petersen, and Stembridge's conjecture on affine Eulerian polynomials for irreducible finite Weyl groups.\n  For the former, we obtain a refinement of Brenti's $q$-Eulerian polynomials of type $D$, and then show that these refined Eulerian polynomials satisfy certain recurrence relation. By using the Routh--Hurwitz theory and the recurrence relation, we prove that these polynomials form a mutu"},"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":"1401.6273","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-24T07:33:10Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"822e07c5ce5e02e1baa7b6ba0702b853a513e8a27e0c99246aa53fb0502ad7aa","abstract_canon_sha256":"313a76a9e2c97dd7f9dd8f0831c9f38892554994077f7ed38d3645a533379e64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:12.644751Z","signature_b64":"JhKN9YsEQjMWDsQMODmTvrBubxNFpbp4ifdfuAV9mX5D7PeNA+y62nA2YDXhFLcVYLFm7qjE8XnFHJJb//+WCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5794d98788b2ae8d5d1b4d80debd359988d370c02a3b4b2c69f8182fedf5277","last_reissued_at":"2026-05-18T03:01:12.643966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:12.643966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mutual Interlacing and Eulerian-like Polynomials for Weyl Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Arthur L.B. Yang, Philip B. Zhang","submitted_at":"2014-01-24T07:33:10Z","abstract_excerpt":"We use the method of mutual interlacing to prove two conjectures on the real-rootedness of Eulerian-like polynomials: Brenti's conjecture on $q$-Eulerian polynomials for Weyl groups of type $D$, and Dilks, Petersen, and Stembridge's conjecture on affine Eulerian polynomials for irreducible finite Weyl groups.\n  For the former, we obtain a refinement of Brenti's $q$-Eulerian polynomials of type $D$, and then show that these refined Eulerian polynomials satisfy certain recurrence relation. By using the Routh--Hurwitz theory and the recurrence relation, we prove that these polynomials form a mutu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6273","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":""},"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":"1401.6273","created_at":"2026-05-18T03:01:12.644104+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.6273v1","created_at":"2026-05-18T03:01:12.644104+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6273","created_at":"2026-05-18T03:01:12.644104+00:00"},{"alias_kind":"pith_short_12","alias_value":"2V4U3GDYRMVO","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2V4U3GDYRMVORVOR","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2V4U3GDY","created_at":"2026-05-18T12:28:11.866339+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/2V4U3GDYRMVORVORWTMA326TLG","json":"https://pith.science/pith/2V4U3GDYRMVORVORWTMA326TLG.json","graph_json":"https://pith.science/api/pith-number/2V4U3GDYRMVORVORWTMA326TLG/graph.json","events_json":"https://pith.science/api/pith-number/2V4U3GDYRMVORVORWTMA326TLG/events.json","paper":"https://pith.science/paper/2V4U3GDY"},"agent_actions":{"view_html":"https://pith.science/pith/2V4U3GDYRMVORVORWTMA326TLG","download_json":"https://pith.science/pith/2V4U3GDYRMVORVORWTMA326TLG.json","view_paper":"https://pith.science/paper/2V4U3GDY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.6273&json=true","fetch_graph":"https://pith.science/api/pith-number/2V4U3GDYRMVORVORWTMA326TLG/graph.json","fetch_events":"https://pith.science/api/pith-number/2V4U3GDYRMVORVORWTMA326TLG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2V4U3GDYRMVORVORWTMA326TLG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2V4U3GDYRMVORVORWTMA326TLG/action/storage_attestation","attest_author":"https://pith.science/pith/2V4U3GDYRMVORVORWTMA326TLG/action/author_attestation","sign_citation":"https://pith.science/pith/2V4U3GDYRMVORVORWTMA326TLG/action/citation_signature","submit_replication":"https://pith.science/pith/2V4U3GDYRMVORVORWTMA326TLG/action/replication_record"}},"created_at":"2026-05-18T03:01:12.644104+00:00","updated_at":"2026-05-18T03:01:12.644104+00:00"}