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arXiv · 1607.00733

Generalized multiplicities of edge ideals

Ali Alilooee·Ivan Soprunov·Javid Validashti
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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 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.

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Ali Alilooee, Ivan Soprunov, Javid Validashti. 2016-07-04. Generalized multiplicities of edge ideals. https://arxiv.org/abs/1607.00733

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