4 papers · 1 filter
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…
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})…
On the Lucky and Displacement Statistics of Stirling Permutations
Laura Colmenarejo, Aleyah Dawkins, Jennifer Elder +5
Stirling permutations are parking functions, and we investigate two parking function statistics in the context of these objects: lucky cars and displacement. Among our results, we…
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…