Journal of Algebraic Combinatorics
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 that the j-multiplicity is multiplicative over the connected components of a hypergraph, and we explicitly relate the j-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.
Alilooee, Alie; Soprunov, Ivan; and Validashti, Javid, "Generalized Multiplicities of Edge Ideals" (2018). Mathematics Faculty Publications. 278.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10801-017-0781-3