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Hilbert Series of Graphs, Hypergraphs, and Monomial Ideals
- 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 |
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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. |
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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 |