@inproceedings{22299,
  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.},
  author       = {Edelsbrunner, Herbert and Lipiński, Michał and Mrozek, Marian and Soriano Trigueros, Manuel and Zimin, Fedor},
  booktitle    = {42nd International Symposium on Computational Geometry},
  isbn         = {9783959774185},
  issn         = {1868-8969},
  keywords     = {Algebraic topology, Lefschetz complexes, persistent homology, vines and vineyards, birth-death pairs, shallow pairs, relations, partial orders, transpositions, Theory of computation → Computational geometry},
  location     = {New Brunswick, NJ, United States},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{The depth poset under transpositions in the filter}},
  doi          = {10.4230/LIPICS.SOCG.2026.41},
  volume       = {367},
  year         = {2026},
}