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We are interested in the bilinear transformations that compute the coefficient sequence of $\\fh(\\fa\\ast\\fb)(t)$ from those of $\\fh(\\fa)(t)$ and $\\fh(\\fb)(t)$, where $\\sum_{n\\geq 0}a_nb_n t^n=\\frac{\\fh(\\fa\\ast\\fb)(t)}{("},"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":"1303.5358","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-21T18:21:57Z","cross_cats_sorted":[],"title_canon_sha256":"193fd0dc9fb4af644b8e762ccc944df07d2ec772b8f6dad71cddbf2d264fd33d","abstract_canon_sha256":"cb7c8292deb230abc2a064be4526e6cfb2cb0789295acf4a2fa444847d944456"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:13.064395Z","signature_b64":"V3Awgi3RCgsriFdeMhm3xbrpF1L13bOvct73p5l1NNptGLMzzXt/+JrfHBIPqyGzMguoAUbgg5uk/ki5jL3tDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c64490d5fc485e0c0f1c823aec2152cc2c1558482601e6ac2494f5d8d32a1115","last_reissued_at":"2026-05-18T03:30:13.063843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:13.063843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectra and eigenvectors of the Segre transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ilse Fischer, Martina Kubitzke","submitted_at":"2013-03-21T18:21:57Z","abstract_excerpt":"Given two sequences $\\fa=(a_n)_{n\\geq 0}$ and $\\fb=(b_n)_{n\\geq 0}$ of complex numbers such that their generating series are of the form $\\sum_{n\\geq 0}a_n t^n=\\frac{\\fh(\\fa)(t)}{(1-t)^{d_{\\fa}}}$ and $\\sum_{n\\geq 0}b_n t^n=\\frac{\\fh(\\fb)(t)}{(1-t)^{d_{\\fb}}}$, where $\\fh(\\fa)(t)$ and $\\fh(\\fb)(t)$ are polynomials, we consider their Segre product $\\fa\\ast\\fb=(a_nb_n)_{n\\geq 0}$. We are interested in the bilinear transformations that compute the coefficient sequence of $\\fh(\\fa\\ast\\fb)(t)$ from those of $\\fh(\\fa)(t)$ and $\\fh(\\fb)(t)$, where $\\sum_{n\\geq 0}a_nb_n t^n=\\frac{\\fh(\\fa\\ast\\fb)(t)}{("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5358","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":"1303.5358","created_at":"2026-05-18T03:30:13.063929+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.5358v1","created_at":"2026-05-18T03:30:13.063929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5358","created_at":"2026-05-18T03:30:13.063929+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZCJBVP4JBPA","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZCJBVP4JBPAYDY4","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZCJBVP4","created_at":"2026-05-18T12:28:09.283467+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/YZCJBVP4JBPAYDY4QI5OYIKSZQ","json":"https://pith.science/pith/YZCJBVP4JBPAYDY4QI5OYIKSZQ.json","graph_json":"https://pith.science/api/pith-number/YZCJBVP4JBPAYDY4QI5OYIKSZQ/graph.json","events_json":"https://pith.science/api/pith-number/YZCJBVP4JBPAYDY4QI5OYIKSZQ/events.json","paper":"https://pith.science/paper/YZCJBVP4"},"agent_actions":{"view_html":"https://pith.science/pith/YZCJBVP4JBPAYDY4QI5OYIKSZQ","download_json":"https://pith.science/pith/YZCJBVP4JBPAYDY4QI5OYIKSZQ.json","view_paper":"https://pith.science/paper/YZCJBVP4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.5358&json=true","fetch_graph":"https://pith.science/api/pith-number/YZCJBVP4JBPAYDY4QI5OYIKSZQ/graph.json","fetch_events":"https://pith.science/api/pith-number/YZCJBVP4JBPAYDY4QI5OYIKSZQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZCJBVP4JBPAYDY4QI5OYIKSZQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZCJBVP4JBPAYDY4QI5OYIKSZQ/action/storage_attestation","attest_author":"https://pith.science/pith/YZCJBVP4JBPAYDY4QI5OYIKSZQ/action/author_attestation","sign_citation":"https://pith.science/pith/YZCJBVP4JBPAYDY4QI5OYIKSZQ/action/citation_signature","submit_replication":"https://pith.science/pith/YZCJBVP4JBPAYDY4QI5OYIKSZQ/action/replication_record"}},"created_at":"2026-05-18T03:30:13.063929+00:00","updated_at":"2026-05-18T03:30:13.063929+00:00"}