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A lower bound for the interleaving distance on persistence vector spaces is given in terms of rank invariants.
G. Carlsson. Topology and data
2009
Earlier work this paper cites.
A. Cerri, B. Di Fabio, M. Ferri, P. Frosini, and C. Landi, Betti numbers in multidimensional persistent homology are stable functions
2013
Cited alongside, same era.
M. Lesnick, The theory of the interleaving distance on multidimensional persistence modules
Cited in the paper.
U. Bauer and M. Lesnick, Induced matchings of barcodes and the algebraic stability of persistence
2014
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