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math.CO2024
Maximum Persistent Betti Numbers of Čech Complexes
Herbert Edelsbrunner, Matthew Kahle, Shu Kanazawa
This note proves that only a linear number of holes in a Čech complex of points in can persist over an interval of constant length. Specifically, for any fixed d…
math.AT2024
Merge Trees of Periodic Filtrations
Herbert Edelsbrunner, Teresa Heiss
Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are…