{"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"}