Approximation by interval-decomposables and interval resolutions of persistence modules

DOI10.1016/j.jpaa.2023.107397arXiv2207.03663MaRDI QIDQ6161071

Emerson G. Escolar, Hideto Asashiba, Michio Yoshiwaki, Ken Nakashima

Publication date: 26 June 2023

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.03663

zbMATH Keywords

representation theorymultidimensional persistencerelative homological algebra

Mathematics Subject Classification ID

Persistent homology and applications, topological data analysis (55N31) Representations of quivers and partially ordered sets (16G20)

Related Items (2)

Computing generalized rank invariant for 2-parameter persistence modules via zigzag persistence and its applications ⋮ Homological approximations in persistence theory

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Iyama's finiteness theorem via strongly quasi-hereditary algebras.
• The theory of multidimensional persistence
• Algebra VIII: Representations of finite-dimensional algebras. Transl. from the Russian
• Radical embeddings and representation dimension.
• Topological persistence and simplification
• Generalized persistence diagrams for persistence modules over posets
• On interval decomposability of \(2\)D persistence modules
• Cotorsion torsion triples and the representation theory of filtered hierarchical clustering
• Every 1D persistence module is a restriction of some indecomposable 2D persistence module
• Representation dimension as a relative homological invariant of stable equivalence.
• On the representation type of tensor product algebras
• Tame triangular matrix algebras
• Finiteness of representation dimension
• Decomposition of pointwise finite-dimensional persistence modules
• Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension
• Decomposition of persistence modules
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• Persistence modules on commutative ladders of finite type

This page was built for publication: Approximation by interval-decomposables and interval resolutions of persistence modules