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.

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)

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