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There is a classification theorem for zigzag persistence vector spaces over a field k analogous to that for ordinary persistence.
“It now turns out that there is a classification theorem for zigzag persistence vector spaces over a field k analogous to that for ordinary persistence.”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Gabriel (1972)
For any zigzag persistence k-vector space of finite type, there is an isomorphism V ≅ ⊕ V_{[m_i,n_i]} for some pairs of integers, and the decomposition is unique up to reordering.
“Then, for any zigzag persistence k -vector space V . of finite type, there is an isomorphism”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Gabriel (1972)
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- Authors
- Gabriel, P.
- Affiliations
- University of Bonn (DE)
- Corresponding author
- Gabriel, Peter
- Venue
- manuscripta mathematica
- Published
- 1972-03
- Volume
- 6
- Issue
- 1
- Pages
- 71-103
- ISSN
- 0025-2611 (ISSN-L)
- 1432-1785
- OpenAlex
- W1964172127
- Cited by
- 771
- References
- 2
- Citations by year
- 2026: 14 · 2025: 26 · 2024: 24 · 2023: 33 · 2022: 39 · 2021: 41 · 2020: 39 · 2019: 33 · 2018: 36 · 2017: 19 · 2016: 36 · 2015: 17 · 2014: 28 · 2013: 27 · 2012: 22
- FWCI
- 11.38
- Type
- journal article
- Language
- de
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- manuscripta mathematica (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Physical Sciences › Mathematics › Algebra and Number Theory › Rings, Modules, and Algebras
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Finite Group Theory Research
- Keywords
- linear representations
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