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Article
Generalized Multiplicities of Edge Ideals
Journal of Algebraic Combinatorics
  • Alie Alilooee, Western Illinois University
  • Ivan Soprunov, Cleveland State University
  • Javid Validashti, Cleveland State University
Document Type
Article
Publication Date
5-1-2018
Disciplines
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
Citation Information
Alie Alilooee, Ivan Soprunov and Javid Validashti. "Generalized Multiplicities of Edge Ideals" Journal of Algebraic Combinatorics Vol. 47 Iss. 3 (2018) p. 441 - 472 ISSN: 0925-9899
Available at: http://works.bepress.com/ivan-soprunov/8/