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Set $\\sigma _j:=\\sum _{1\\leq i_1<\\cdots <i_j\\leq n-1}a_{i_1}\\cdots a_{i_j}$. The eigenvalues of the affine mapping $(c_1,\\ldots ,c_{n-1})\\mapsto (\\sigma _1,\\ldots ,\\sigma _{n-1})$ are positive rational numbers and its eigenvectors are defined by hyperbolic polynomials (i.e. with real roots only). In the present paper we prove interlac"},"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":"1504.02321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-04-09T14:13:18Z","cross_cats_sorted":[],"title_canon_sha256":"8d4578260dbfe13059942a1ef70211f1f099ccf29685cd61dc65648a8d9c4a86","abstract_canon_sha256":"75563d3c1fff9449a9606d06d4752a979c4ab688abafb89bdcd010fe7c4193e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:15.424141Z","signature_b64":"fXv4Zih8otwt9dKrxMKUVAJHn53RssUpjnOI9VnzR1GNG1b1l3KPtgV9MT8nKz2LAV17aOHcikGBMBlOIBkECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a40036ce17b70d5737da2bd62e020a9069fd66d43e76af1baa1ba8f237a90c01","last_reissued_at":"2026-05-18T02:19:15.423389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:15.423389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interlacing properties and the Schur-Szeg\\H{o} composition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Vladimir Petrov Kostov","submitted_at":"2015-04-09T14:13:18Z","abstract_excerpt":"Each degree $n$ polynomial in one variable of the form $(x+1)(x^{n-1}+c_1x^{n-2}+\\cdots +c_{n-1})$ is representable in a unique way as a Schur-Szeg\\H{o} composition of $n-1$ polynomials of the form $(x+1)^{n-1}(x+a_i)$, see \\cite{Ko1}, \\cite{AlKo} and \\cite{Ko2}. Set $\\sigma _j:=\\sum _{1\\leq i_1<\\cdots <i_j\\leq n-1}a_{i_1}\\cdots a_{i_j}$. The eigenvalues of the affine mapping $(c_1,\\ldots ,c_{n-1})\\mapsto (\\sigma _1,\\ldots ,\\sigma _{n-1})$ are positive rational numbers and its eigenvectors are defined by hyperbolic polynomials (i.e. with real roots only). In the present paper we prove interlac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02321","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":"1504.02321","created_at":"2026-05-18T02:19:15.423521+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.02321v1","created_at":"2026-05-18T02:19:15.423521+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02321","created_at":"2026-05-18T02:19:15.423521+00:00"},{"alias_kind":"pith_short_12","alias_value":"UQADNTQXW4GV","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UQADNTQXW4GVON62","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UQADNTQX","created_at":"2026-05-18T12:29:44.643036+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/UQADNTQXW4GVON62FPLC4AQKSB","json":"https://pith.science/pith/UQADNTQXW4GVON62FPLC4AQKSB.json","graph_json":"https://pith.science/api/pith-number/UQADNTQXW4GVON62FPLC4AQKSB/graph.json","events_json":"https://pith.science/api/pith-number/UQADNTQXW4GVON62FPLC4AQKSB/events.json","paper":"https://pith.science/paper/UQADNTQX"},"agent_actions":{"view_html":"https://pith.science/pith/UQADNTQXW4GVON62FPLC4AQKSB","download_json":"https://pith.science/pith/UQADNTQXW4GVON62FPLC4AQKSB.json","view_paper":"https://pith.science/paper/UQADNTQX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.02321&json=true","fetch_graph":"https://pith.science/api/pith-number/UQADNTQXW4GVON62FPLC4AQKSB/graph.json","fetch_events":"https://pith.science/api/pith-number/UQADNTQXW4GVON62FPLC4AQKSB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UQADNTQXW4GVON62FPLC4AQKSB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UQADNTQXW4GVON62FPLC4AQKSB/action/storage_attestation","attest_author":"https://pith.science/pith/UQADNTQXW4GVON62FPLC4AQKSB/action/author_attestation","sign_citation":"https://pith.science/pith/UQADNTQXW4GVON62FPLC4AQKSB/action/citation_signature","submit_replication":"https://pith.science/pith/UQADNTQXW4GVON62FPLC4AQKSB/action/replication_record"}},"created_at":"2026-05-18T02:19:15.423521+00:00","updated_at":"2026-05-18T02:19:15.423521+00:00"}