Chip-firing groups of iterated cones

TL;DR

This paper investigates the asymptotic behavior of the chip-firing group associated with iterated cones over a finite graph, revealing structural patterns as the cone parameter grows.

Contribution

It introduces a detailed analysis of the chip-firing groups of iterated cones, providing new insights into their asymptotic structure and properties.

Findings

Characterization of the asymptotic structure of $ ext{Pic}^0( ext{Gamma}_n)$

Identification of structural patterns in chip-firing groups for iterated cones

Insights into the growth and behavior of chip-firing groups as $n$ increases

Abstract

Let $\Gamma$ be a finite graph and let $\Gamma_n$ be the "$n$th cone over $\Gamma$" (i.e., the join of $\Gamma$ and the complete graph $K_n$). We study the asymptotic structure of the chip-firing group $\text{Pic}^0(\Gamma_n)$.