Keywords
hilbert series, hilbert function, graph ring, path, cycle, h-polynomial
Abstract
The Hilbert Series of a finitely-generated graded R-module, M, is a series which is often given in the form a rational function in the variable, t. This series encodes a great many invariant properties of the module M. In this dissertation, I study the Hilbert series and related invariants of the graph rings for paths and cycles. By utilizing a result of Kyle Trainor, I am able to examine the Hilbert series and the related invariants of these graph rings recursively through second and higher-order difference equations. This technique allows me to extract information about the Hilbert series that has not been previously well known, and for which other techniques are limited.
Completion Date
2025
Semester
Summer
Committee Chair
Joseph Brennan
Degree
Doctor of Philosophy (Ph.D.)
College
College of Sciences
Department
Mathematics
Format
Identifier
DP0029598
Language
English
Document Type
Thesis
Campus Location
Orlando (Main) Campus
STARS Citation
Nielander, Tiffany, "The Hilbert Series of Paths, Cycles, and Related Graphs" (2025). Graduate Thesis and Dissertation post-2024. 357.
https://stars.library.ucf.edu/etd2024/357