Title

Generalized Multiplicities of Edge Ideals

Document Type

Article

Publication Date

7-21-2017

Publication Title

Journal of Algebraic Combinatorics

Abstract

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.

Original Citation

Alilooee, A., Soprunov, I. & Validashti, J. J Algebr Comb (2017). https://doi.org/10.1007/s10801-017-0781-3

DOI

10.1007/s10801-017-0781-3

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