Poincaré series of some hypergraph algebras

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 Poincaré series $P_{R_H}(t)={\sum }_{i=1}^{\infty }{\dim }_k{\mathrm{Tor}}_i^{R_H}(k,k)t^i$ for some hypergraphs generalizing lines, cycles, and stars. We finish by calculating the graded Betti numbers and the Poincaré series of the graph algebra of the wheel graph.

Six pages

References in corpus (1)

• Betti Numbers of Graph Ideals

Cited by in corpus (1)

• Algebraic properties of product of graphs