Document Type

Article

Publication Date

5-2018

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.

DOI

10.1007/s10801-017-0781-3

Version

Postprint

Volume

47

Issue

3

Available for download on Wednesday, May 01, 2019

Included in

Mathematics Commons

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