---
OA_place: publisher
OA_type: gold
_id: '22299'
abstract:
- lang: eng
text: 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.
acknowledgement: "The authors thank Jakub Leśkiewicz and Bartosz Furmanek for discussions\r\nthat
helped improve the paper. Herbert Edelsbrunner: DFG Collaborative Research Center
TRR 109, Austrian Science\r\nFund (FWF), grant no. I 02979-N35\r\nMichał Lipiński:
European Union’s Horizon 2020 research and innovation programme under the\r\nMarie
Skłodowska-Curie Grant Agreement No. 101034413\r\nMarian Mrozek: Polish National
Science Center under Opus Grant 2019/35/B/ST1/00874 and Opus\r\nGrant 2025/57/B/ST1/00550"
alternative_title:
- LIPIcs
article_number: 41:1-41:18
article_processing_charge: Yes
arxiv: 1
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Michał
full_name: Lipiński, Michał
id: dfffb474-4317-11ee-8f5c-fe3fc95a425e
last_name: Lipiński
orcid: 0000-0001-9789-9750
- first_name: Marian
full_name: Mrozek, Marian
last_name: Mrozek
orcid: 0000-0002-0619-6417
- first_name: Manuel
full_name: Soriano Trigueros, Manuel
id: 15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8
last_name: Soriano Trigueros
orcid: 0000-0003-2449-1433
- first_name: Fedor
full_name: Zimin, Fedor
id: afd27eda-91c1-11f0-aad8-c6edbec24c04
last_name: Zimin
citation:
ama: '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'
apa: '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'
chicago: 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.
ieee: 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.
ista: '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.'
mla: 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.
short: H. Edelsbrunner, M. Lipiński, M. Mrozek, M. Soriano Trigueros, F. Zimin,
in:, 42nd International Symposium on Computational Geometry, Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2026.
conference:
end_date: 2026-06-05
location: New Brunswick, NJ, United States
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2026-06-02
corr_author: '1'
das_tickbox: '0'
date_created: 2026-07-13T09:56:38Z
date_published: 2026-05-27T00:00:00Z
date_updated: 2026-08-12T09:02:56Z
day: '27'
ddc:
- '500'
department:
- _id: HeEd
- _id: GradSch
doi: 10.4230/LIPICS.SOCG.2026.41
ec_funded: 1
external_id:
arxiv:
- '2511.21961'
file:
- access_level: open_access
checksum: 9dfb96ee66985c724b499b0e5888dc8e
content_type: application/pdf
creator: dernst
date_created: 2026-07-14T06:08:05Z
date_updated: 2026-07-14T06:08:05Z
file_id: '22329'
file_name: 2026_LIPIcSSoCG_Edelsbrunner.pdf
file_size: 2902144
relation: main_file
success: 1
file_date_updated: 2026-07-14T06:08:05Z
fulldoi: https://doi.org/10.4230/LIPICS.SOCG.2026.41
has_accepted_license: '1'
intvolume: ' 367'
keyword:
- Algebraic topology
- Lefschetz complexes
- persistent homology
- vines and vineyards
- birth-death pairs
- shallow pairs
- relations
- partial orders
- transpositions
- Theory of computation → Computational geometry
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: 42nd International Symposium on Computational Geometry
publication_identifier:
eissn:
- 1868-8969
isbn:
- '9783959774185'
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: The depth poset under transpositions in the filter
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 367
year: '2026'
...