Abstract
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.
Notes
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Graduation Date
2018
Semester
Summer
Advisor
Brennan, Joseph
Degree
Doctor of Philosophy (Ph.D.)
College
College of Sciences
Department
Mathematics
Degree Program
Mathematics
Format
application/pdf
Identifier
CFE0007202
URL
http://purl.fcla.edu/fcla/etd/CFE0007258
Language
English
Release Date
August 2018
Length of Campus-only Access
None
Access Status
Doctoral Dissertation (Open Access)
STARS Citation
Trainor, Kyle, "Hilbert Series of Graphs, Hypergraphs, and Monomial Ideals" (2018). Electronic Theses and Dissertations. 6005.
https://stars.library.ucf.edu/etd/6005