Betti numbers of hypergraphs

Details Betti numbers of hypergraphs Betti numbers of hypergraphs

2007-11-21

arxiv.org/abs/0711.3368v3

Mathematics

Commutative Algebra

To appear in Communications in Algebra

Scientific paper

In this paper we study some algebraic properties of hypergraphs, in particula their Betti numbers. We define some different types of complete hypergraphs, which to the best of our knowledge, are not previously considered in the literature. Also, in a natural way, we define a product on hypergraphs, which in a sense is dual to the join operation on simplicial complexes. For such product, we give a general formula for the Betti numbers, which specializes neatly in case of linear resolutions.

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