For any fixed c ≥ 1, there exist finite metric spaces whose Vietoris-Rips filtration cannot be c-approximated by any finitely presented construction of linear size; for c < √2, exponential size is required.
Lower bounds on the homology of Vietoris– Rips complexes of hypercube graphs.Bulletin of the Malaysian Mathematical Sciences Society, 47(3):72, 2024
2 Pith papers cite this work, alongside 8 external citations. Polarity classification is still indexing.
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For hypercube Vietoris–Rips complexes, the paper derives connectivity and coconnectivity bounds and constructs explicit cohomology classes with cross-polytope representatives, but key theorems contain errors.
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Lower Bounds for Approximating the Vietoris-Rips Filtration
For any fixed c ≥ 1, there exist finite metric spaces whose Vietoris-Rips filtration cannot be c-approximated by any finitely presented construction of linear size; for c < √2, exponential size is required.
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Cohomological properties of the Vietoris--Rips Complex of a Hypercube Graph
For hypercube Vietoris–Rips complexes, the paper derives connectivity and coconnectivity bounds and constructs explicit cohomology classes with cross-polytope representatives, but key theorems contain errors.