Stable set rings which are Gorenstein on the punctured spectrum

TL;DR

This paper investigates the conditions under which stable set rings of perfect graphs are Gorenstein on the punctured spectrum, revealing combinatorial characterizations and exploring properties of Cohen--Macaulay graded algebras.

Contribution

It provides a combinatorial description of perfect graphs with Gorenstein stable set rings on the punctured spectrum and analyzes the independence of Cohen--Macaulay type and residue.

Findings

Characterization of perfect graphs with Gorenstein stable set rings

Stable set rings are Gorenstein on the punctured spectrum under specific combinatorial conditions

Cohen--Macaulay type and residue are largely independent in graded algebras

Abstract

The non-Gorenstein locus of stable set rings of finite simple perfect graphs is studied. We describe combinatorially those perfect graphs whose stable set rings are Gorenstein on the punctured spectrum. In addition, we show that, in general, for Cohen--Macaulay graded algebras, their Cohen--Macaulay type and residue are largely independent.