14 citations · 34 across the 16 of their papers we have counts for
17 papers
Critical groups of arithmetical structures on star graphs and complete graphs
Kassie Archer, Alexander Diaz-Lopez, Darren Glass +1
An arithmetical structure on a finite, connected graph without loops is an assignment of positive integers to the vertices that satisfies certain conditions. Associated to each of…
Chip-Firing Games and Critical Groups
Darren Glass, Nathan Kaplan
In this expository article intended to be accessible to undergraduate students we introduce a finite abelian group that can be associated to any finite connected graph. This group…
Arithmetical Structures on Paths With a Doubled Edge
Darren Glass, Joshua Wagner
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and…
Arithmetical structures on bidents
Kassie Archer, Abigail Bishop, Alexander Diaz-Lopez +3
An arithmetical structure on a finite, connected graph is a pair of vectors with positive integer entries for which $(\operatorname{diag}(\mathbf{d})…
Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
Dan Boneh, Darren Glass, Daniel Krashen +5
We describe a framework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n >= 2. Our approach is based on the problem of computing i…
Counting Arithmetical Structures on Paths and Cycles
Benjamin Braun, Hugo Corrales, Scott Corry +6
Let be a finite, simple, connected graph. An arithmetical structure on is a pair of positive integer vectors such that $(\mathrm{diag}(\mathbf{d})-A…