Chip-Firing on Trees of Loops

  • Sameer Kailasa
  • Vivian Kuperberg
  • Nicholas Wawrykow
DOI: https://doi.org/10.37236/7244
Keywords: Chip-firing, Metric graphs, Brill-Noether generality

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.
Published
2018-01-25
Issue
Volume 25, Issue 1 (2018)
Article Number
P1.19