Critical groups of iterated cones

TL;DR

This paper investigates the structure of the critical group associated with iterated cones over a finite graph, contributing to divisor and sandpile theory by analyzing their algebraic properties.

Contribution

It provides new insights into the structure of critical groups for iterated cones, a topic not extensively explored before.

Findings

Characterization of the critical group structure for G_n

Connections established between iterated cones and sandpile models

New algebraic properties identified for critical groups of iterated cones

Abstract

Let G be a finite graph, and let G_n be the n-th iterated cone over G. We study the structure of the critical group of G_n arising in divisor and sandpile theory.