31 citations · 67 across the 10 of their papers we have counts for
13 papers
A memorial tribute: Adriano Garsia (1928--2024)
Hélène Barcelo, François Bergeron, Nantel Bergeron +15
Adriano Mario Garsia was born in Tunis on August 20, 1928, to a Tunisian-Italian family. He lived on a farm there until the end of World War II, then moved to Rome. After finishing…
On the vanishing of discrete singular cubical homology for graphs
Helene Barcelo, Curtis Greene, Abdul Salam Jarrah +1
We prove that if G is a graph without 3-cycles and 4-cycles, then the discrete cubical homology of G is trivial in dimension d, for all d\ge 2. We also construct a sequence { G_d }…
Homology groups of cubical sets with connections
Helene Barcelo, Curtis Greene, Abdul Salam Jarrah +1
Toward defining commutative cubes in all dimensions, Brown and Spencer introduced the notion of "connection" as a new kind of degeneracy. In this paper, for a cubical set with conn…
Algebraic Voting Theory & Representations of
Hélène Barcelo, Megan Bernstein, Sarah Bockting-Conrad +3
We consider the problem of selecting an -member committee made up of one of candidates from each of distinct departments. Using an algebraic approach, we analyze positio…
Discrete Cubical and Path Homologies of Graphs
Helene Barcelo, Curtis Greene, Abdul Salam Jarrah +1
In this paper we study and compare two homology theories for (simple and undirected) graphs. The first, which was developed by Barcelo, Caprano, and White, is based on graph maps f…
Discrete Homology Theory for Metric Spaces
Helene Barcelo, Valerio Capraro, Jacob A. White
In this paper we define and study a notion of discrete homology theory for metric spaces. Instead of working with simplicial homology, our chain complexes are given by Lipschitz ma…