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Journal Articles Algebras and Representation Theory Year : 2023

Local characterizations for decomposability of 2-parameter persistence modules

Abstract

We investigate the existence of sufficient local conditions under which poset representations decompose as direct sums of indecomposables from a given class. In our work, the indexing poset is the product of two totally ordered sets, corresponding to the setting of 2-parameter persistence in topological data analysis. Our indecomposables of interest belong to the so-called interval modules, which by definition are indicator representations of intervals in the poset. While the whole class of interval modules does not admit such a local characterization, we show that the subclass of rectangle modules does admit one and that it is, in some precise sense, the largest subclass to do so.
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Dates and versions

hal-02995822 , version 1 (30-01-2023)

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Magnus Bakke Botnan, Vadim Lebovici, Steve Oudot. Local characterizations for decomposability of 2-parameter persistence modules. Algebras and Representation Theory, In press, ⟨10.1007/s10468-022-10189-4⟩. ⟨hal-02995822⟩
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