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We determine the Poincar\\'e series $P_{R_H}(t)=\\sum_{i=1}^\\infty\\dim_k{\\rm Tor}_i^{R_H}(k,k)t^i$ for some hypergraphs generalizing lines, cycles, and stars. We finish by calculating the graded Betti numbers and the Poincar\\'e series of the graph algebra of the wheel graph."},"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":"0901.1534","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-01-12T10:08:55Z","cross_cats_sorted":[],"title_canon_sha256":"58844be7448a5e362c000a0515f744dd690b867f25533114394bc071d5e54f4e","abstract_canon_sha256":"5b1c7b14bd7bde2f6571625b4f78f6fe4aa7787e20ac88e4b1f6c3c4524ba1dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:43.636502Z","signature_b64":"a22Tg1F/Pi+n3g+iNk8BIdbSHQtssawR+R5WF6zID6u5Kb1Sts4VpqmK29Rijn2u/lSWlH4/+1fH39TwYS2LCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b73bee0894ab595206c28f482363b77b6b79b96dd095cf7b84d56f7cd5264f3","last_reissued_at":"2026-05-18T01:30:43.634375Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:43.634375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poincar\\'e series of some hypergraph algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Eric Emtander, Fatemeh Mohammadi, Ralf Fr\\\"oberg, Somayeh Moradi","submitted_at":"2009-01-12T10:08:55Z","abstract_excerpt":"A hypergraph $H=(V,E)$, where $V=\\{x_1,...,x_n\\}$ and $E\\subseteq 2^V$ defines a hypergraph algebra $R_H=k[x_1,...,x_n]/(x_{i_1}... x_{i_k}; \\{i_1,...,i_k\\}\\in E)$. All our hypergraphs are $d$-uniform, i.e., $|e_i|=d$ for all $e_i\\in E$. We determine the Poincar\\'e series $P_{R_H}(t)=\\sum_{i=1}^\\infty\\dim_k{\\rm Tor}_i^{R_H}(k,k)t^i$ for some hypergraphs generalizing lines, cycles, and stars. We finish by calculating the graded Betti numbers and the Poincar\\'e series of the graph algebra of the wheel graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1534","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":"0901.1534","created_at":"2026-05-18T01:30:43.634460+00:00"},{"alias_kind":"arxiv_version","alias_value":"0901.1534v1","created_at":"2026-05-18T01:30:43.634460+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1534","created_at":"2026-05-18T01:30:43.634460+00:00"},{"alias_kind":"pith_short_12","alias_value":"JNZ35YEJJK2Z","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"JNZ35YEJJK2ZKIDM","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"JNZ35YEJ","created_at":"2026-05-18T12:26:00.592388+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/JNZ35YEJJK2ZKIDMFD2IENR3O6","json":"https://pith.science/pith/JNZ35YEJJK2ZKIDMFD2IENR3O6.json","graph_json":"https://pith.science/api/pith-number/JNZ35YEJJK2ZKIDMFD2IENR3O6/graph.json","events_json":"https://pith.science/api/pith-number/JNZ35YEJJK2ZKIDMFD2IENR3O6/events.json","paper":"https://pith.science/paper/JNZ35YEJ"},"agent_actions":{"view_html":"https://pith.science/pith/JNZ35YEJJK2ZKIDMFD2IENR3O6","download_json":"https://pith.science/pith/JNZ35YEJJK2ZKIDMFD2IENR3O6.json","view_paper":"https://pith.science/paper/JNZ35YEJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0901.1534&json=true","fetch_graph":"https://pith.science/api/pith-number/JNZ35YEJJK2ZKIDMFD2IENR3O6/graph.json","fetch_events":"https://pith.science/api/pith-number/JNZ35YEJJK2ZKIDMFD2IENR3O6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JNZ35YEJJK2ZKIDMFD2IENR3O6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JNZ35YEJJK2ZKIDMFD2IENR3O6/action/storage_attestation","attest_author":"https://pith.science/pith/JNZ35YEJJK2ZKIDMFD2IENR3O6/action/author_attestation","sign_citation":"https://pith.science/pith/JNZ35YEJJK2ZKIDMFD2IENR3O6/action/citation_signature","submit_replication":"https://pith.science/pith/JNZ35YEJJK2ZKIDMFD2IENR3O6/action/replication_record"}},"created_at":"2026-05-18T01:30:43.634460+00:00","updated_at":"2026-05-18T01:30:43.634460+00:00"}