The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
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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An Introduction to Homological Algebra
Weibel, C. A. (1994) · Cambridge University Press eBooks · doi:10.1017/cbo9781139644136 · Cited by 3,905
Mumford, D., Fogarty, J., & Kirwan, F. (1994) · Springer Grundlehren · doi:10.1007/978-3-642-57916-5 · Cited by 2,564
Gromov, M. (1987) · Mathematical Sciences Research Institute Publications · doi:10.1007/978-1-4613-9586-7_3 · Cited by 1,817
Topological Persistence and Simplification
Edelsbrunner, Letscher, & Zomorodian (2002) · Discrete & Computational Geometry · doi:10.1007/s00454-002-2885-2 · Cited by 1,779
Introduction to Commutative Algebra.
Lewis, D., McDonald, B. R., Atiyah, M. F., & MacDonald, I. G. (1970) · American Mathematical Monthly · doi:10.2307/2316241 · Cited by 1,709
Zomorodian, A., & Carlsson, G. (2005) · Discrete & Computational Geometry · doi:10.1007/s00454-004-1146-y · Cited by 1,591
Self-citationBarcodes: the persistent topology of data
Ghrist, R. (2007) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-07-01191-3 · Cited by 1,236
On the Local Behavior of Spaces of Natural Images
Carlsson, G., Ishkhanov, T., de Silva, V., & Zomorodian, A. (2008) · International Journal of Computer Vision · doi:10.1007/s11263-007-0056-x · Cited by 477
Self-citationPERSISTENCE BARCODES FOR SHAPES
CARLSSON, G., ZOMORODIAN, A., COLLINS, A., & GUIBAS, L. J. (2005) · International Journal of Shape Modeling · doi:10.1142/s0218654305000761 · Cited by 287
Self-citationThe Nonlinear Statistics of High-Contrast Patches in Natural Images
Lee, A. B., Pedersen, K. S., & Mumford, D. (2003) · International Journal of Computer Vision · doi:10.1023/a:1023705401078 · Cited by 234
Research works printed but not linked: 2
- de Silva, V., Carlsson, G.: Topological estimation using witness complexes. In: Proceedings of IEEE/Eurographics Symposium on Point-Based Graphics, pp. 157–166 (2004)
- Gyulassy, A., Natarajan, V., Pascucci, V., Bremer, P.T., Hamann, B.: Topology-based simplification for feature extraction from 3D scalar fields. In: Proceedings of IEEE Visualization, pp. 275–280 (2005)
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Carlsson, G. (2009) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-09-01249-x · Cited by 2,302
Self-citationNetworks beyond pairwise interactions: Structure and dynamics
Battiston, F., Cencetti, G., Iacopini, I., Latora, V., Lucas, M., Patania, A., Young, J.-G., & Petri, G. (2020) · Physics Reports · doi:10.1016/j.physrep.2020.05.004 · Cited by 1,879
Networks beyond pairwise interactions: Structure and dynamics
Battiston, F., Cencetti, G., Iacopini, I., Latora, V., Lucas, M., Patania, A., Young, J., & Petri, G. (2020) · UCL Discovery (University College London) · Cited by 1,179
A roadmap for the computation of persistent homology
Otter, N., Porter, M. A., Tillmann, U., Grindrod, P., & Harrington, H. A. (2017) · EPJ Data Science · doi:10.1140/epjds/s13688-017-0109-5 · Cited by 769
What are higher-order networks?
Bick, C., Gross, E., Harrington, H. A., & Schaub, M. T. (2023) · SIAM Review · doi:10.1137/21m1414024 · Cited by 420
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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