3 papers
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.DS2024
A Complete Invariant for Shift Equivalence for Boolean Matrices and Finite Relations
Ethan Akin, Marian Mrozek, Mateusz Przybylski +1
We give a complete invariant for shift equivalence for Boolean matrices (equivalently finite relations), in terms of the period, the induced partial order on recurrent components,…
math.AT2023
The poset of cancellations induced by gradient dynamics in a filtered Lefschetz complex
Herbert Edelsbrunner, Michał Lipiński, Marian Mrozek +1
Motivated by questions about simplification of topology, we take a discrete approach to the dependency of simplifying operations, using methods based on combinatorial gradient dyna…