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- W3196000381 abstract "In this paper, we define the homological Morse numbers of a filtered cell complex in terms of relative homology of nested filtration pieces, and derive inequalities relating these numbers to the Betti tables of the multi-parameter persistence modules of the considered filtration. Using the Mayer-Vietoris spectral sequence we first obtain strong and weak Morse inequalities involving the above quantities, and then we improve the weak inequalities achieving a sharp lower bound for homological Morse numbers. Furthermore, we prove a sharp upper bound for homological Morse numbers, expressed again in terms of the Betti tables." @default.
- W3196000381 created "2021-08-30" @default.
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- W3196000381 date "2023-07-01" @default.
- W3196000381 modified "2023-10-10" @default.
- W3196000381 title "Morse inequalities for the Koszul complex of multi-persistence" @default.
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- W3196000381 doi "https://doi.org/10.1016/j.jpaa.2023.107319" @default.
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