The Hilbert Series of Paths, Cycles, and Related Graphs
Year: 2025
Type: article
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.
Author: Nielander, Tiffany
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7111883994
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