On the Hilbert series of vertex cover algebras of Cohen-Macaulay bipartite graphs

TL;DR

This paper investigates the Hilbert function and series of vertex cover algebras associated with Cohen-Macaulay bipartite graphs, providing insights into their algebraic and combinatorial properties.

Contribution

It offers a detailed analysis of the Hilbert series of vertex cover algebras for Cohen-Macaulay bipartite graphs, a topic not extensively explored before.

Findings

Derived explicit formulas for Hilbert series

Connected algebraic properties to graph Cohen-Macaulayness

Enhanced understanding of vertex cover algebra structures

Abstract

We study the Hilbert function and the Hilbert series of the vertex cover algebra $A(G)$, where $G$ is a Cohen-Macaulay bipartite graph.