{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:J76D6PEGPWJJGSTRHPV6VKDP2X","short_pith_number":"pith:J76D6PEG","schema_version":"1.0","canonical_sha256":"4ffc3f3c867d92934a713bebeaa86fd5f67d63f002465c6996923ec304869ca9","source":{"kind":"arxiv","id":"1203.0791","version":2},"attestation_state":"computed","paper":{"title":"Stable multivariate $W$-Eulerian polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mirk\\'o Visontai, Nathan Williams","submitted_at":"2012-03-05T00:39:10Z","abstract_excerpt":"We prove a multivariate strengthening of Brenti's result that every root of the Eulerian polynomial of type $B$ is real. Our proof combines a refinement of the descent statistic for signed permutations with the notion of real stability-a generalization of real-rootedness to polynomials in multiple variables. The key is that our refined multivariate Eulerian polynomials satisfy a recurrence given by a stability-preserving linear operator. Our results extend naturally to colored permutations, and we also give stable generalizations of recent real-rootedness results due to Dilks, Petersen, and St"},"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":"1203.0791","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-05T00:39:10Z","cross_cats_sorted":[],"title_canon_sha256":"29660bad180ca89e9887fcc08298b4ffe76cf4c0b1c2dc447d849729a227ce9f","abstract_canon_sha256":"e4ec91d48a4cd2c4f139024749941893ba9b2acdcdf9689611af804c819880cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:00.531222Z","signature_b64":"fPEn7GlrfgSzD5/W1BxiuUJMT1dsmRkQa6x5eDWI/p9tegilhhSh9z5BpIQkyiD0RDP1CBygq/gZ37rvEogTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ffc3f3c867d92934a713bebeaa86fd5f67d63f002465c6996923ec304869ca9","last_reissued_at":"2026-05-18T02:32:00.530611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:00.530611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable multivariate $W$-Eulerian polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mirk\\'o Visontai, Nathan Williams","submitted_at":"2012-03-05T00:39:10Z","abstract_excerpt":"We prove a multivariate strengthening of Brenti's result that every root of the Eulerian polynomial of type $B$ is real. Our proof combines a refinement of the descent statistic for signed permutations with the notion of real stability-a generalization of real-rootedness to polynomials in multiple variables. The key is that our refined multivariate Eulerian polynomials satisfy a recurrence given by a stability-preserving linear operator. Our results extend naturally to colored permutations, and we also give stable generalizations of recent real-rootedness results due to Dilks, Petersen, and St"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0791","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":"1203.0791","created_at":"2026-05-18T02:32:00.530699+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.0791v2","created_at":"2026-05-18T02:32:00.530699+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0791","created_at":"2026-05-18T02:32:00.530699+00:00"},{"alias_kind":"pith_short_12","alias_value":"J76D6PEGPWJJ","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"J76D6PEGPWJJGSTR","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"J76D6PEG","created_at":"2026-05-18T12:27:11.947152+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/J76D6PEGPWJJGSTRHPV6VKDP2X","json":"https://pith.science/pith/J76D6PEGPWJJGSTRHPV6VKDP2X.json","graph_json":"https://pith.science/api/pith-number/J76D6PEGPWJJGSTRHPV6VKDP2X/graph.json","events_json":"https://pith.science/api/pith-number/J76D6PEGPWJJGSTRHPV6VKDP2X/events.json","paper":"https://pith.science/paper/J76D6PEG"},"agent_actions":{"view_html":"https://pith.science/pith/J76D6PEGPWJJGSTRHPV6VKDP2X","download_json":"https://pith.science/pith/J76D6PEGPWJJGSTRHPV6VKDP2X.json","view_paper":"https://pith.science/paper/J76D6PEG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.0791&json=true","fetch_graph":"https://pith.science/api/pith-number/J76D6PEGPWJJGSTRHPV6VKDP2X/graph.json","fetch_events":"https://pith.science/api/pith-number/J76D6PEGPWJJGSTRHPV6VKDP2X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J76D6PEGPWJJGSTRHPV6VKDP2X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J76D6PEGPWJJGSTRHPV6VKDP2X/action/storage_attestation","attest_author":"https://pith.science/pith/J76D6PEGPWJJGSTRHPV6VKDP2X/action/author_attestation","sign_citation":"https://pith.science/pith/J76D6PEGPWJJGSTRHPV6VKDP2X/action/citation_signature","submit_replication":"https://pith.science/pith/J76D6PEGPWJJGSTRHPV6VKDP2X/action/replication_record"}},"created_at":"2026-05-18T02:32:00.530699+00:00","updated_at":"2026-05-18T02:32:00.530699+00:00"}