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math.AT2025
The Depth Poset under Transpositions in the Filter
Herbert Edelsbrunner, Michał Lipiński, Marian Mrozek +2
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…
math.DS2025
Conley-Morse persistence barcode: a homological signature of combinatorial bifurcations
Tamal K. Dey, Michał Lipiński, Manuel Soriano-Trigueros
Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations…