Signed barcodes for multi-parameter persistence via rank decompositions and rank-exact resolutions

MB Botnan, S Oppermann, S Oudot - Foundations of Computational …, 2024 - Springer
In this paper, we introduce the signed barcode, a new visual representation of the global
structure of the rank invariant of a multi-parameter persistence module or, more generally, of …

Invariants of persistence modules defined by order-embeddings

C Amiot, T Brüstle, EJ Hanson - arXiv preprint arXiv:2402.09190, 2024 - arxiv.org
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 …

[PDF][PDF] ON INTERVAL GLOBAL DIMENSION OF POSETS: A CHARACTERIZATION OF CASE 0

T AOKI, EG ESCOLAR, S TADA - on Ring Theory and …, 2024 - ring-theory-japan.com
We study the relative homological algebra of posets with respect to the intervals. We
introduce our recent research on the properties of the supports of interval approximations …