0100491594

open access

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On approximation of 2D persistence modules by interval-decomposables

English (英語)

Journal of Computational Algebra

6–7

100007

Elsevier

2023-09-04

2024-09-17

n this work, we propose a new invariant for 2D persistence modules called the compressed multiplicity and show that it generalizes the notions of the dimension vector and the rank invariant. In addition, for a 2D persistence module M, we propose an “interval-decomposable replacement” δ*(M) (in the split Grothendieck group of the category of persistence modules), which is expressed by a pair of interval-decomposable modules, that is, its positive and negative parts. We show that M is interval-decomposable if and only if δ*(M) is equal to M in the split Grothendieck group. Furthermore, even for modules M not necessarily interval-decomposable, δ*(M) preserves the dimension vector and the rank invariant of M. In addition, we provide an algorithm to compute δ*(M) (a high-level algorithm in the general case, and a detailed algorithm for the size case).

Intervals

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