The depth poset under transpositions in the filter
Edelsbrunner H, Lipiński M, Mrozek M, Soriano Trigueros M, Zimin F. 2026. The depth poset under transpositions in the filter. 42nd International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 367, 41:1-41:18.
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Author
Edelsbrunner, HerbertISTA 
;
Lipiński, MichałISTA ;
Mrozek, Marian ;
Soriano Trigueros, ManuelISTA ;
Zimin, FedorISTA
;
Lipiński, MichałISTA ;
Mrozek, Marian ;
Soriano Trigueros, ManuelISTA ;
Zimin, FedorISTACorresponding author has ISTA affiliation
Department
Grant
Series Title
LIPIcs
Abstract
The depth poset of a filtered Lefschetz complex reflects the dependencies between the cancellations of different shallow birth-death pairs. Using the fast algorithms for computing the depth poset in [Edelsbrunner et al., 2026] and for updating the persistence diagram under transpositions in [Cohen-Steiner et al., 2006], we give a complete case analysis of how transpositions of cells in the filter affect the depth poset. In addition, we present statistics on the depth poset for random point data and its sensitivity to the transpositions that occur in random straight-line homotopies.
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Publishing Year
Date Published
2026-05-27
Proceedings Title
42nd International Symposium on Computational Geometry
Publisher
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Acknowledgement
The authors thank Jakub Leśkiewicz and Bartosz Furmanek for discussions
that helped improve the paper. Herbert Edelsbrunner: DFG Collaborative Research Center TRR 109, Austrian Science
Fund (FWF), grant no. I 02979-N35
Michał Lipiński: European Union’s Horizon 2020 research and innovation programme under the
Marie Skłodowska-Curie Grant Agreement No. 101034413
Marian Mrozek: Polish National Science Center under Opus Grant 2019/35/B/ST1/00874 and Opus
Grant 2025/57/B/ST1/00550
Volume
367
Article Number
41:1-41:18
Conference
SoCG: Symposium on Computational Geometry
Conference Location
New Brunswick, NJ, United States
Conference Date
2026-06-02 – 2026-06-05
ISBN
eISSN
IST-REx-ID
Cite this
Edelsbrunner H, Lipiński M, Mrozek M, Soriano Trigueros M, Zimin F. The depth poset under transpositions in the filter. In: 42nd International Symposium on Computational Geometry. Vol 367. Schloss Dagstuhl – Leibniz-Zentrum für Informatik; 2026. doi:10.4230/LIPICS.SOCG.2026.41
Edelsbrunner, H., Lipiński, M., Mrozek, M., Soriano Trigueros, M., & Zimin, F. (2026). The depth poset under transpositions in the filter. In 42nd International Symposium on Computational Geometry (Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.SOCG.2026.41
Edelsbrunner, Herbert, Michał Lipiński, Marian Mrozek, Manuel Soriano Trigueros, and Fedor Zimin. “The Depth Poset under Transpositions in the Filter.” In 42nd International Symposium on Computational Geometry, Vol. 367. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2026. https://doi.org/10.4230/LIPICS.SOCG.2026.41.
H. Edelsbrunner, M. Lipiński, M. Mrozek, M. Soriano Trigueros, and F. Zimin, “The depth poset under transpositions in the filter,” in 42nd International Symposium on Computational Geometry, New Brunswick, NJ, United States, 2026, vol. 367.
Edelsbrunner H, Lipiński M, Mrozek M, Soriano Trigueros M, Zimin F. 2026. The depth poset under transpositions in the filter. 42nd International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 367, 41:1-41:18.
Edelsbrunner, Herbert, et al. “The Depth Poset under Transpositions in the Filter.” 42nd International Symposium on Computational Geometry, vol. 367, 41:1-41:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2026, doi:10.4230/LIPICS.SOCG.2026.41.
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