Homological algebra of modules over posets is developed, as closely parallel as possible to
that of finitely generated modules over noetherian commutative rings, in the direction of finite …

In topological data analysis, two-parameter persistence can be studied using the
representation theory of the 2d commutative grid, the tensor product of two Dynkin quivers of …

We study the decomposition of zero-dimensional persistence modules, viewed as functors
valued in the category of vector spaces factorizing through sets. Instead of working directly at …

We study the interplay between algebraic and metric properties of multi-parameter
persistence modules (linear representations of the poset $\mathbf {R}^ n $ with $ n\geq 2$) …

We first introduce the notion of meta-rank for a 2-parameter persistence module, an invariant
that captures the information behind images of morphisms between 1D slices of the module …

We present the shift-dimension of multipersistence modules and investigate its algebraic
properties. This gives rise to a new invariant of multigraded modules over the multivariate …

Understanding the structure of indecomposable $ n $-dimensional persistence modules is a
difficult problem, yet is foundational for studying multipersistence. To this end, Buchet and …

We consider maximal non-l-intertwining collections, which are a higher-dimensional version
of the maximal non-crossing collections which give clusters of Plücker coordinates in the …

In this paper, we study pointwise finite-dimensional (pfd) $2 $-parameter persistence
modules where each module admits a finite convex isotopy subdivision. We show that a pfd …

In the contemporary computing landscape, the effective utilization of data has emerged as a
primary driving force. Nonetheless, handling data with intricate structures, non-Euclidean …