---
res:
  bibo_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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Herbert
      foaf_name: Edelsbrunner, Herbert
      foaf_surname: Edelsbrunner
      foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-9823-6833
  - foaf_Person:
      foaf_givenName: Michał
      foaf_name: Lipiński, Michał
      foaf_surname: Lipiński
      foaf_workInfoHomepage: http://www.librecat.org/personId=dfffb474-4317-11ee-8f5c-fe3fc95a425e
    orcid: 0000-0001-9789-9750
  - foaf_Person:
      foaf_givenName: Marian
      foaf_name: Mrozek, Marian
      foaf_surname: Mrozek
    orcid: 0000-0002-0619-6417
  - foaf_Person:
      foaf_givenName: Manuel
      foaf_name: Soriano Trigueros, Manuel
      foaf_surname: Soriano Trigueros
      foaf_workInfoHomepage: http://www.librecat.org/personId=15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8
    orcid: 0000-0003-2449-1433
  - foaf_Person:
      foaf_givenName: Fedor
      foaf_name: Zimin, Fedor
      foaf_surname: Zimin
      foaf_workInfoHomepage: http://www.librecat.org/personId=afd27eda-91c1-11f0-aad8-c6edbec24c04
  bibo_doi: 10.4230/LIPICS.SOCG.2026.41
  bibo_volume: 367
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1868-8969
  - http://id.crossref.org/issn/9783959774185
  dct_language: eng
  dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@
  dct_subject:
  - Algebraic topology
  - Lefschetz complexes
  - persistent homology
  - vines and vineyards
  - birth-death pairs
  - shallow pairs
  - relations
  - partial orders
  - transpositions
  - Theory of computation → Computational geometry
  dct_title: The depth poset under transpositions in the filter@
...