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math.CO2025

Grassmannian Persistence Diagrams: Special Properties in the 1-Parameter Setting

Aziz Burak Gülen, Facundo Mémoli, Zhengchao Wan

In this paper, we explore the discriminative power of Grassmannian persistence diagrams of 1-parameter filtrations, examine their relationships with other related constructions, an…

math.CO2025

Grassmannian Persistence Diagrams

Aziz Burak Gülen, Facundo Mémoli, Zhengchao Wan

We introduce Orthogonal Möbius Inversion , a concept analogous to Möbius inversion on finite posets, which is applicable to order-preservings functions from a finite…

math.CO2024

Extremal spherical polytopes and Borsuk's conjecture

Mikhail Katz, Facundo Mémoli, Qingsong Wang

We generate anti-self-polar polytopes via a numerical implementation of the gradient flow induced by the diameter functional on the space of all finite subsets of the sphere, and p…