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math.AT2025
Persistent Cycle Representatives and Generalized Landscapes for Codimension 1 Persistent Homology
Fabian Lenzen, Leon Renkin
For a filtered simplicial complex embedded in , the merge tree of the complement of induces a forest structure on the persistent homology via Ale…
math.CO2025
An Empirically Fast Las Vegas Algorithm for Algebraic Shifting
Antony Della Vecchia, Michael Joswig, Fabian Lenzen
Improved algorithms for computing (partial and full) exterior algebraic shifts of hypergraphs and simplicial complexes are presented. The main benefit is in positive characteristic…