3 papers
math.AT2026
Counting Barcodes with the same Betti Curve
Henry Ashley, Håvard Bakke Bjerkevik, Justin Curry +2
This paper considers an important inverse problem in topological data analysis (TDA): How many different barcodes produce the same Betti curve? Equivalently, given a function $β\co…
math.CO2025
The Topological Structures of the Orders of Hypergraphs
Robert E. Green, Cliff A. Joslyn, Audun Myers +2
We provide first a categorical exploration of, and then completion of the mapping of the relationships among, three fundamental perspectives on binary relations: as the incidence m…
cs.SI2024
Understanding High-Order Network Structure using Permissible Walks on Attributed Hypergraphs
Enzo Battistella, Sean English, Robert Green +6
Hypergraphs have been a recent focus of study in mathematical data science as a tool to understand complex networks with high-order connections. One question of particular relevanc…