Chip-Firing on Trees of Loops

Sameer Kailasa, Vivian Kuperberg, Nicholas Wawrykow


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.


Chip-firing; Metric graphs; Brill-Noether generality

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