A class of transversal polymatroids with Gorenstein base ring

TL;DR

This paper characterizes a specific class of transversal polymatroids with Gorenstein base rings using polyhedral geometry, and computes their algebraic invariants such as the a-invariant and Hilbert series.

Contribution

It introduces a new class of transversal polymatroids with Gorenstein base rings and applies polyhedral geometry tools for their characterization.

Findings

Characterization of the Gorenstein property using the Danilov-Stanley theorem

Explicit computation of the a-invariant for the base rings

Calculation of the Hilbert series for the class

Abstract

In this paper, the principal tool to describe transversal polymatroids with Gorenstein base ring is polyhedral geometry, especially the $Danilov-Stanley$ theorem for the characterization of canonical module. Also, we compute the $a-invariant$ and the Hilbert series of base ring associated to this class of transversal polymatroids.