conference paper published yes Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Michał Lipiński author dfffb474-4317-11ee-8f5c-fe3fc95a425e0000-0001-9789-9750 Marian Mrozek author 0000-0002-0619-6417 Manuel Soriano Trigueros author 15ebd7cf-15bf-11ee-aebd-bb4bb5121ea80000-0003-2449-1433 Fedor Zimin author afd27eda-91c1-11f0-aad8-c6edbec24c04 HeEd department GradSch department SoCG: Symposium on Computational Geometry Persistence and stability of geometric complexes project IST-BRIDGE: International postdoctoral program project 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. https://research-explorer.ista.ac.at/download/22299/22329/2026_LIPIcSSoCG_Edelsbrunner.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Schloss Dagstuhl - Leibniz-Zentrum für Informatik2026New Brunswick, NJ, United States eng Algebraic topologyLefschetz complexespersistent homologyvines and vineyardsbirth-death pairsshallow pairsrelationspartial orderstranspositionsTheory of computation → Computational geometry 1868-8969 9783959774185 2511.2196110.4230/LIPICS.SOCG.2026.41 367 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. Edelsbrunner H, Lipiński M, Mrozek M, Soriano Trigueros M, Zimin F. The depth poset under transpositions in the filter. In: <i>42nd International Symposium on Computational Geometry</i>. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href="https://doi.org/10.4230/LIPICS.SOCG.2026.41">10.4230/LIPICS.SOCG.2026.41</a> 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.” <i>42nd International Symposium on Computational Geometry</i>, vol. 367, 41:1-41:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href="https://doi.org/10.4230/LIPICS.SOCG.2026.41">10.4230/LIPICS.SOCG.2026.41</a>. H. Edelsbrunner, M. Lipiński, M. Mrozek, M. Soriano Trigueros, and F. Zimin, “The depth poset under transpositions in the filter,” in <i>42nd International Symposium on Computational Geometry</i>, New Brunswick, NJ, United States, 2026, vol. 367. Edelsbrunner, Herbert, Michał Lipiński, Marian Mrozek, Manuel Soriano Trigueros, and Fedor Zimin. “The Depth Poset under Transpositions in the Filter.” In <i>42nd International Symposium on Computational Geometry</i>, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href="https://doi.org/10.4230/LIPICS.SOCG.2026.41">https://doi.org/10.4230/LIPICS.SOCG.2026.41</a>. Edelsbrunner, H., Lipiński, M., Mrozek, M., Soriano Trigueros, M., &#38; Zimin, F. (2026). The depth poset under transpositions in the filter. In <i>42nd International Symposium on Computational Geometry</i> (Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href="https://doi.org/10.4230/LIPICS.SOCG.2026.41">https://doi.org/10.4230/LIPICS.SOCG.2026.41</a> 222992026-07-13T09:56:38Z2026-08-12T09:02:56Z