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arXiv · 0901.1534

Poincar\'e series of some hypergraph algebras

Eric Emtander·Ralf Fröberg·Fatemeh Mohammadi·Somayeh Moradi
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Abstract

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.

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Eric Emtander, Ralf Fröberg, Fatemeh Mohammadi, Somayeh Moradi. 2009-01-12. Poincar\'e series of some hypergraph algebras. https://arxiv.org/abs/0901.1534

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