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.
Categories: math.AC