The Sandpile Group of a Cone Over a Bi-Coconut Tree
Combinatorics
2026-02-24 v1
Abstract
The sandpile group of a connected graph is a finite abelian group whose cardinality is the number of spanning trees in the graph. We compute the spanning tree number and sandpile group structure for the cone over a bi-coconut tree, generalizing work of Reiner and Smith on the cone over a coconut tree. We also answer one of their questions, by exhibiting a family of trees whose sandpile groups are all cyclic but their number of leaves grows without bound.
Cite
@article{arxiv.2602.18621,
title = {The Sandpile Group of a Cone Over a Bi-Coconut Tree},
author = {Dorian Smith},
journal= {arXiv preprint arXiv:2602.18621},
year = {2026}
}