288 research outputs found
Generalized multiplicities of edge ideals
We explore connections between the generalized multiplicities of square-free
monomial ideals and the combinatorial structure of the underlying hypergraphs
using methods of commutative algebra and polyhedral geometry. For instance, we
show the -multiplicity is multiplicative over the connected components of a
hypergraph, and we explicitly relate the -multiplicity of the edge ideal of
a properly connected uniform hypergraph to the Hilbert-Samuel multiplicity of
its special fiber ring. In addition, we provide general bounds for the
generalized multiplicities of the edge ideals and compute these invariants for
classes of uniform hypergraphs.Comment: 24 pages, 6 figures. The results of Theorem 4.6 and Theorem 9.2 are
now more general. To appear in Journal of Algebraic Combinatoric
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