The Sandpile Group of a Cone Over a Bi-Coconut Tree
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.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Graph theory and applications
Commutative Algebra and Its Applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 20 February 2026
- Language
- EN
- Document type
- Preprint