5 papers
Computing Betti tables and minimal presentations of zero-dimensional persistent homology
Yuan Luo, Dmitriy Morozov, Luis Scoccola
The Betti tables of a multigraded module encode the grades at which there is an algebraic change in the module. Multigraded modules show up in many areas of pure and applied mathem…
Counts and end-curves in two-parameter persistence
Thomas Brüstle, Steve Oudot, Luis Scoccola +1
Given a finite dimensional, bigraded module over the polynomial ring in two variables, we define its two-parameter count, a natural number, and its end-curves, a set of plane curve…
Stabilization of the Spread-Global Dimension
Benjamin Blanchette, Justin Desrochers, Eric J. Hanson +1
Motivated by constructions from applied topology, there has been recent interest in the homological algebra of linear representations of posets, particularly in the context of homo…
Multi-Parameter Persistence Modules are Generically Indecomposable
Ulrich Bauer, Luis Scoccola
Algebraic persistence studies persistence modules (typically, linear representations of the poset with ) and the algebraic relationships between persistenc…
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…