Classifications of Cohen-Macaulay modules - The base ring associated to a transversal polymatroid

TL;DR

This thesis investigates the algebraic properties of base rings linked to transversal polymatroids, a specific class of discrete polymatroids, expanding understanding of their structure and classification.

Contribution

It provides a detailed study of the base rings associated with transversal polymatroids, a subclass of discrete polymatroids, highlighting their algebraic and combinatorial properties.

Findings

Characterization of base rings for transversal polymatroids

Connections between polymatroid structure and algebraic properties

Extensions of discrete polymatroid theory

Abstract

In this thesis, we focus on the study of the base rings associated to some transversal polymatroids. A transversal polymatroid is a special kind of discrete polymatroid. Discrete polymatroids were introduced by Herzog and Hibi \cite{HH} in 2002.