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Generalized multiplicities of edge ideals

Authors
  • Alilooee, Ali
  • Soprunov, Ivan
  • Validashti, Javid
Type
Preprint
Publication Date
Jul 03, 2016
Submission Date
Jul 03, 2016
Identifiers
arXiv ID: 1607.00733
Source
arXiv
License
Yellow
External links

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 the $j$-multiplicity is multiplicative over the connected components of a uniform hypergraph, and we 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 we compute these invariants for classes of uniform hypergraphs.

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