## Betti Numbers of Graph Ideals, Dissertation, Univ

- S. Jacques
- 2004

- Published 2009

A hypergraph H = (V, E), where V = {x1, . . . , xn} and E ⊆ 2 V defines a hypergraph algebra RH = k[x1, . . . , xn]/(xi1 · · ·xik ; {i1, . . . , ik} ∈ E). All our hypergraphs are d-uniform, i.e., |ei| = d for all ei ∈ E. We determine the Poincaré series PRH (t) = P ∞ i=1 dimk Tor RH i (k, k)t 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.

@inproceedings{Emtander2009JaN2,
title={Ja n 20 09 Poincar{\'e} series of some hypergraph algebras},
author={E . Emtander and Farajollah Mohammadi and Sirous Moradi},
year={2009}
}