Persistence modules on commutative ladders of finite type

DOI10.1007/s00454-015-9746-2zbMath1411.16011OpenAlexW2112471150MaRDI QIDQ5964222

Yasuaki Hiraoka, Emerson G. Escolar

Publication date: 29 February 2016

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-015-9746-2

zbMATH Keywords

representation theoryAuslander-Reiten theorycommutative ladderpersistence moduletopological data analysis

Mathematics Subject Classification ID

Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of associative Artinian rings (16G10) Other homology theories in algebraic topology (55N35)

Related Items (15)

On interval decomposability of \(2\)D persistence modules ⋮ Decomposition theory of modules: the case of Kronecker algebra ⋮ Decomposition of pointwise finite-dimensional 𝕊1 persistence modules ⋮ The space of barcode bases for persistence modules ⋮ Partial matchings induced by morphisms between persistence modules ⋮ Computing generalized rank invariant for 2-parameter persistence modules via zigzag persistence and its applications ⋮ Approximation by interval-decomposables and interval resolutions of persistence modules ⋮ Homological approximations in persistence theory ⋮ Matrix method for persistence modules on commutative ladders of finite type ⋮ Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension ⋮ \(\tau\)-tilting finite triangular matrix algebras ⋮ Report on the finiteness of silting objects ⋮ THE COMBINATORICS OF TENSOR PRODUCTS OF HIGHER AUSLANDER ALGEBRAS OF TYPEA ⋮ Decomposing filtered chain complexes: geometry behind barcoding algorithms ⋮ On rectangle-decomposable 2-parameter persistence modules

Uses Software

• CGAL

Cites Work

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• Morse theory for filtrations and efficient computation of persistent homology
• Tame algebras and integral quadratic forms
• Stability of persistence diagrams
• The theory of multidimensional persistence
• Computational homology
• Computing persistent homology
• Topological persistence and simplification
• The union of balls and its dual shape
• Zigzag persistence
• Categorification of persistent homology
• A topological measurement of protein compressibility
• Unzerlegbare Darstellungen. I. (Indecomposable representations. I)
• Computing Persistence Modules on Commutative Ladders of Finite Type
• Topology and data
• Tame triangular matrix algebras
• Decomposition of pointwise finite-dimensional persistence modules
• Proximity of persistence modules and their diagrams
• Computing Decompositions of Modules over Finite-Dimensional Algebras

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