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Showing 1 to 2 of 2 for “"Persistence Modules"”.
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On the representation theory of persistence modules
… we study representation theoretic aspects of persistence modules. The first subject is an investigation of the spectrum of the category of vector space representations of a totally ordered set $T$: We show the existence of and determine the spectrum of this category in the sense of Krause and …
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Generalized Rank Invariant : Structure, Möbius Inversion, and Persistence Diagram
… Unlike the one-parameter case, multiparameter persistence modules lack a complete discrete invariant analogous to barcodes, and their classification requires tools that can capture subtle interactions across the indexing poset. In this thesis we develop and study a generalized rank invariant …