# Chip-firing on trees of loops

## TL;DR

This paper investigates the Brill-Noether properties of trees of loops, showing that only paths of loops are Brill-Noether general, and explores various notions of generality for these graphs.

## Contribution

It demonstrates that Brill-Noether generality fails for most trees of loops, except for paths of loops, and analyzes different notions of generality in this context.

## Key findings

- Paths of loops are Brill-Noether general.
- Most trees of loops are not Brill-Noether general.
- Various notions of generality are examined for these graphs.

## Abstract

Cools, Draisma, Payne, and Robeva proved that generic metric graphs that are "paths of loops" are Brill-Noether general. We show that Brill-Noether generality does not hold for "trees of loops": the only trees of loops that are Brill-Noether general are paths of loops. We study various notions of generality and examine which of these graphs satisfy them.