3 papers
math.CO2026
The Sandpile Group of a Cone Over a Bi-Coconut Tree
Dorian Smith
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 g…
math.CO2024
Sandpile groups for cones over trees
Victor Reiner, Dorian Smith
Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their grou…
math.CO2024
Arithmetical Structures on Coconut Trees
Alexander Diaz-Lopez, Brian Ha, Pamela E. Harris +3
If G is a finite connected graph, then an arithmetical structure on is a pair of vectors with positive integer entries such that $(\diag(\mathbf{d})…