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The Theory of Multidimensional Persistence
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“it is shown in Carlsson and Zomorodian (2009) that the isomorphism classification of n -persistence vector spaces with the parameter set restricted to Z n + is identical to the classification of n -graded modules over the n -graded ring k [ t 1 , . . . , t n ].”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Carlsson and Zomorodian (2009)
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Metadata
- Authors
- Carlsson, G., & Zomorodian, A.
- Affiliations
- Stanford University (US)
- Dartmouth College (US)
- Corresponding author
- Zomorodian, Afra
- ORCID
- Carlsson, Gunnar
- Venue
- Discrete & Computational Geometry
- Published
- 2009-04-24
- Volume
- 42
- Issue
- 1
- Pages
- 71-93
- ISSN
- 0179-5376 (ISSN-L)
- 1432-0444
- OpenAlex
- W4251980118
- Cited by
- 270
- References
- 19
- Citations by year
- 2026: 11 · 2025: 29 · 2024: 21 · 2023: 25 · 2022: 31 · 2021: 23 · 2020: 22 · 2019: 13 · 2018: 16 · 2017: 13 · 2016: 12 · 2015: 12 · 2014: 11 · 2013: 8 · 2012: 9
- FWCI
- 7.16
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Discrete & Computational Geometry (publishedVersion)
- Funders
- National Science Foundation (0354543)
- Defense Advanced Research Projects Agency
- Office of Naval Research
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Keywords
- persistent homology, Betti numbers, discrete invariants, topological data analysis
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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