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math.AT2022★ 9 cited
On the bottleneck stability of rank decompositions of multi-parameter persistence modules
Magnus Bakke Botnan, Steffen Oppermann, Steve Oudot +1
A significant part of modern topological data analysis is concerned with the design and study of algebraic invariants of poset representations -- often referred to as multi-paramet…
math.AT2021★ 14 cited
On the stability of multigraded Betti numbers and Hilbert functions
Steve Oudot, Luis Scoccola
Multigraded Betti numbers are one of the simplest invariants of multiparameter persistence modules. This invariant is useful in theory -- it completely determines the Hilbert funct…