In this work, we propose a new invariant for 2D persistence modules called the compressed
multiplicity and show that it generalizes the notions of the dimension vector and the rank …

A significant part of modern topological data analysis is concerned with the design and study
of algebraic invariants of poset representations—often referred to as persistence modules …

In this work, we propose a new invariant for $2 $ D persistence modules called the
compressed multiplicity and show that it generalizes the notions of the dimension vector and …

One of the main objectives of topological data analysis is the study of discrete invariants for
persistence modules, in particular when dealing with multiparameter persistence modules …

Recently, there is growing interest in the use of relative homology algebra to develop
invariants using interval covers and interval resolutions (ie, right minimal approximations …

Persistence modules are representations of products of totally ordered sets in the category
of vector spaces. They appear naturally in the representation theory of algebras, but in …

The Harder-Narasimhan types are a family of discrete isomorphism invariants for
representations of finite quivers. Previously (arXiv: 2303.16075), we evaluated their …

Single parameter persistent homology is a tool that captures the underlying topological
features of a data set by analyzing how its topology varies along a single parameter filtration …

In topological data analysis we study a data set given as a finite point cloud by embedding it
in some parameter-dependent topological spaces, and computing their homology. This can …