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Hilbert Series of Graphs, Hypergraphs, and Monomial Ideals

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Date Issued:
2018
Abstract/Description:
In this dissertation, identities for Hilbert series of quotients of polynomial rings by monomial ideals are explored, beginning in the contexts of graph and hypergraph rings and later generalizing to general monomial ideals. These identities are modeled after constructive identities from graph theory, and can thus be used to construct Hilbert series iteratively from those of smaller algebraic structures.
Title: Hilbert Series of Graphs, Hypergraphs, and Monomial Ideals.
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Name(s): Trainor, Kyle, Author
Brennan, Joseph, Committee Chair
Song, Zixia, Committee Member
Martin, Heath, Committee Member
Morey, Susan, Committee Member
Wocjan, Pawel, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2018
Publisher: University of Central Florida
Language(s): English
Abstract/Description: In this dissertation, identities for Hilbert series of quotients of polynomial rings by monomial ideals are explored, beginning in the contexts of graph and hypergraph rings and later generalizing to general monomial ideals. These identities are modeled after constructive identities from graph theory, and can thus be used to construct Hilbert series iteratively from those of smaller algebraic structures.
Identifier: CFE0007258 (IID), ucf:52176 (fedora)
Note(s): 2018-08-01
Ph.D.
Sciences, Mathematics
Doctoral
This record was generated from author submitted information.
Subject(s): Hilbert Series -- Commutative Algebra -- Graphs -- Hypergraphs
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0007258
Restrictions on Access: public 2018-08-15
Host Institution: UCF

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