2026-09-05T11:55:19Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25847 2026-06-23T12:59:28Z ddc:004 open_access

The Depth Poset Under Transpositions in the Filter Edelsbrunner, Herbert Lipiński, Michał Mrozek, Marian Soriano-Trigueros, Manuel Zimin, Fedor Algebraic topology Lefschetz complexes persistent homology vines and vineyards birth-death pairs shallow pairs relations partial orders transpositions 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Herbert Edelsbrunner and Michał Lipiński and Marian Mrozek and Manuel Soriano-Trigueros and Fedor Zimin 2026 Is Part Of LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2026.41 urn:nbn:de:0030-drops-258479 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.41 eng https://creativecommons.org/licenses/by/4.0/legalcode