Interval Decomposition of Infinite Zigzag Persistence Modules
Representation Theory
2015-07-08 v1 Algebraic Topology
Authors:
Magnus Bakke Botnan
Abstract
We show that every infinite zigzag persistence module decomposes into a direct sum of interval persistence modules.
Cite
@article{arxiv.1507.01899,
title = {Interval Decomposition of Infinite Zigzag Persistence Modules},
author = {Magnus Bakke Botnan},
journal= {arXiv preprint arXiv:1507.01899},
year = {2015}
}
Related papers
View all related →
Representation Theory · Mathematics
Structure of semi-continuous q-tame persistence modules
Maximilian Schmahl
2022-07-05
Representation Theory · Mathematics
Decomposition of pointwise finite-dimensional persistence modules
William Crawley-Boevey
2014-07-30
Algebraic Topology · Mathematics
Bipath Persistence as Zigzag Persistence
Ángel Javier Alonso, Enhao Liu
2025-01-03
Representation Theory · Mathematics
Decomposition of persistence modules
Magnus Bakke Botnan, William Crawley-Boevey
2019-10-07
Algebraic Topology · Mathematics
On interval decomposition of persistence modules
Wee Liang Gan, Nadiya Upegui Keagy
2025-07-03
Representation Theory · Mathematics
Interval Multiplicities of Persistence Modules
Hideto Asashiba, Enhao Liu
2026-05-26
Algebraic Topology · Mathematics
Interval Decomposition of Persistence Modules over a Principal Ideal Domain
Jiajie Luo, Gregory Henselman-Petrusek
2025-10-07
Representation Theory · Mathematics
On Interval Decomposability of 2D Persistence Modules
Hideto Asashiba, Mickaël Buchet, Emerson G. Escolar, Ken Nakashima +1
2021-05-25
Algebraic Topology · Mathematics
Probabilistic Analysis of Multiparameter Persistence Decompositions
Ángel Javier Alonso, Michael Kerber, Primoz Skraba
2024-03-19
Algebraic Topology · Mathematics
Interval Decomposition of Infinite Persistence Modules over a Principal Ideal Domain and Field Choice in Persistent Homology
Jiajie Luo, Gregory Henselman-Petrusek
2026-04-03
Representation Theory · Mathematics
Decomposition of Pointwise Finite-Dimensional S^1 Persistence Modules
Eric J. Hanson, Job D. Rock
2025-06-19
Algebraic Topology · Mathematics
Projective Constant Decompositions of Persistence Modules over Noetherian Rings
Nadiya Upegui Keagy
2026-02-17
Algebraic Topology · Mathematics
Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applications
Tamal K. Dey, Woojin Kim, Facundo Mémoli
2022-04-01
Representation Theory · Mathematics
Local characterizations for decomposability of 2-parameter persistence modules
Magnus Bakke Botnan, Vadim Lebovici, Steve Oudot
2022-12-13
Representation Theory · Mathematics
Decomposition of exact pfd persistence bimodules
Jérémy Cochoy, Steve Oudot
2019-11-28
Algebraic Topology · Mathematics
Parallel computation of interval bases for persistence module decomposition
Alessandro De Gregorio, Marco Guerra, Sara Scaramuccia, Francesco Vaccarino
2025-11-06
Representation Theory · Mathematics
Summand-injectivity of interval covers and monotonicity of interval resolution global dimensions
Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada
2023-11-13
Algebraic Topology · Mathematics
Stability of higher-dimensional interval decomposable persistence modules
Håvard Bakke Bjerkevik
2020-01-22
Representation Theory · Mathematics
Every 1D Persistence Module is a Restriction of Some Indecomposable 2D Persistence Module
Mickaël Buchet, Emerson G. Escolar
2020-03-25
Algebraic Topology · Mathematics
Hyperplane Restrictions of Indecomposable $n$-Dimensional Persistence Modules
Samantha Moore
2020-11-03
Representation Theory · Mathematics
Decomposing Multiparameter Persistence Modules
Tamal K. Dey, Jan Jendrysiak, Michael Kerber
2025-11-25
Algebraic Topology · Mathematics
Decomposing multipersistence modules using functor calculus
Bjørnar Gullikstad Hem
2025-10-09
Computational Geometry · Computer Science
Fast Computation of Zigzag Persistence
Tamal K. Dey, Tao Hou
2022-07-06
Algebraic Topology · Mathematics
Algebraic Stability of Zigzag Persistence Modules
Magnus Bakke Botnan, Michael Lesnick
2018-10-24
Algebraic Topology · Mathematics
Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension
Mickaël Buchet, Emerson G. Escolar
2018-12-20