Cited by 270Topological and Geometric Data AnalysisHomotopy and Cohomology in Algebraic TopologyGeometric and Algebraic Topology

The Theory of Multidimensional Persistence

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Carlsson, Gunnar, Zomorodian, Afra·2009·Discrete & Computational Geometry

Integrity signals

Registry

Crossref · 10.1007/s00454-009-9176-0

Cites

19 of 19 references verified0 citation errors · 0 not checkable

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Claims the paper makes

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  • The isomorphism classification of n-persistence vector spaces with parameter set restricted to Z^n_+ is identical to the classification of n-graded modules over the n-graded ring k[t1,...,tn].

    “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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Authors
Carlsson, G., & Zomorodian, A.
Affiliations
  • Stanford University (US)
  • Dartmouth College (US)
Corresponding author
Zomorodian, Afra
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
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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