62 citations · 144 across the 18 of their papers we have counts for
21 papers
An Algebraic Introduction to Persistence
Ulrich Bauer, Thomas Brüstle, Luis Scoccola
We introduce persistence with an emphasis on its algebraic foundations, using the representation theory of posets. Linear representations of posets arise in several areas of mathem…
Generalized Rank via Minimal Subposet
Thomas Brüstle, Justin Desrochers, Samuel Leblanc
Let be a small, connected category with finite hom-sets. We show that if the embedding of a connected subcategory is both initial and final, then the re…
Decomposing zero-dimensional persistent homology over rooted tree quivers
Riju Bindua, Thomas Brüstle, Luis Scoccola
Given a functor from any category into the category of topological spaces, one obtains a linear representation of the category by post-composing the given functor with a homology f…
Exact structures for persistence modules
Benjamin Blanchette, Thomas Brüstle, Eric J. Hanson
We discuss applications of exact structures and relative homological algebra to the study of invariants of multiparameter persistence modules. This paper is mostly expository, but…
Stratifying systems and Jordan-Hölder extriangulated categories
Thomas Brüstle, Souheila Hassoun, Amit Shah +1
Stratifying systems, which have been defined for module, triangulated and exact categories previously, were developed to produce examples of standardly stratified algebras. A strat…
Homological approximations in persistence theory
Benjamin Blanchette, Thomas Brüstle, Eric J. Hanson
We define a class of invariants, which we call homological invariants, for persistence modules over a finite poset. Informally, a homological invariant is one that respects some ho…