Poincaré Series of some Hypergraph Algebras

• Autores: Eric Emtander, Ralf Fröberg , F. Mohammadi, Somayeh Moradi
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 112, Nº 1, 2013, págs. 5-10
• Idioma: inglés
• DOI: 10.7146/math.scand.a-15229
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• Resumen

  • A hypergraph H=(V,E), where V={x1,…,xn} and E⊆2V 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)=∑∞i=1dimkTorRHi(k,k)ti 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.