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For any $r \\geq 1$ we study the coefficient sequence of the numerator polynomial $h_0(a^{<r >}) +...+ h_{\\lambda'}(a^{<r >}) t^{\\lambda'}$ of the $r$\\textsuperscript{th} Veronese series $a^{<r >}(t) = \\sum_{n \\geq 0} a_{nr} t^n$. Under mild hypothesis we show that the vector of successive differences of this sequence up to the $\\lfloor \\frac{d}{2} \\rfloor$\\textsuperscript{th} entry is the $f$-vector of a simplicial complex for la"},"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":"1108.2852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-14T09:13:23Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"5e0dd38a35f0159f8ff09eb7581f8125bd671162ac75d17710ff811c3e62a63a","abstract_canon_sha256":"bd9a6531ce77d60564780beb58c1f721d2f020ed163e5bad909e30c74688ffaf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:29.051291Z","signature_b64":"MYlJb/6yHyH2cNdlljFpyAnkpB9nw92sk8mmaAsPxaqJHm1jE+mBuo0k2T5zNpKK9YF6Tg11/WgZtQ/DNUbdAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c24883164f7986007c8c38a65ad7bc412aae1df07926227707ea0515cce3db2b","last_reissued_at":"2026-05-18T04:15:29.050902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:29.050902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enumerative $g$-theorems for the Veronese construction for formal power series and graded algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Martina Kubitzke, Volkmar Welker","submitted_at":"2011-08-14T09:13:23Z","abstract_excerpt":"Let $(a_n)_{n \\geq 0}$ be a sequence of integers such that its generating series satisfies $\\sum_{n \\geq 0} a_nt^n = \\frac{h(t)}{(1-t)^d}$ for some polynomial $h(t)$. For any $r \\geq 1$ we study the coefficient sequence of the numerator polynomial $h_0(a^{<r >}) +...+ h_{\\lambda'}(a^{<r >}) t^{\\lambda'}$ of the $r$\\textsuperscript{th} Veronese series $a^{<r >}(t) = \\sum_{n \\geq 0} a_{nr} t^n$. Under mild hypothesis we show that the vector of successive differences of this sequence up to the $\\lfloor \\frac{d}{2} \\rfloor$\\textsuperscript{th} entry is the $f$-vector of a simplicial complex for la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2852","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":"1108.2852","created_at":"2026-05-18T04:15:29.050954+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.2852v1","created_at":"2026-05-18T04:15:29.050954+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2852","created_at":"2026-05-18T04:15:29.050954+00:00"},{"alias_kind":"pith_short_12","alias_value":"YJEIGFSPPGDA","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YJEIGFSPPGDAA7EM","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YJEIGFSP","created_at":"2026-05-18T12:26:47.523578+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/YJEIGFSPPGDAA7EMHCTFVV54IE","json":"https://pith.science/pith/YJEIGFSPPGDAA7EMHCTFVV54IE.json","graph_json":"https://pith.science/api/pith-number/YJEIGFSPPGDAA7EMHCTFVV54IE/graph.json","events_json":"https://pith.science/api/pith-number/YJEIGFSPPGDAA7EMHCTFVV54IE/events.json","paper":"https://pith.science/paper/YJEIGFSP"},"agent_actions":{"view_html":"https://pith.science/pith/YJEIGFSPPGDAA7EMHCTFVV54IE","download_json":"https://pith.science/pith/YJEIGFSPPGDAA7EMHCTFVV54IE.json","view_paper":"https://pith.science/paper/YJEIGFSP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.2852&json=true","fetch_graph":"https://pith.science/api/pith-number/YJEIGFSPPGDAA7EMHCTFVV54IE/graph.json","fetch_events":"https://pith.science/api/pith-number/YJEIGFSPPGDAA7EMHCTFVV54IE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YJEIGFSPPGDAA7EMHCTFVV54IE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YJEIGFSPPGDAA7EMHCTFVV54IE/action/storage_attestation","attest_author":"https://pith.science/pith/YJEIGFSPPGDAA7EMHCTFVV54IE/action/author_attestation","sign_citation":"https://pith.science/pith/YJEIGFSPPGDAA7EMHCTFVV54IE/action/citation_signature","submit_replication":"https://pith.science/pith/YJEIGFSPPGDAA7EMHCTFVV54IE/action/replication_record"}},"created_at":"2026-05-18T04:15:29.050954+00:00","updated_at":"2026-05-18T04:15:29.050954+00:00"}