Interleavings and matchings as representations
| Autor: | Emerson G. Escolar, Michio Yoshiwaki, Killian Meehan |
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| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
Hardware_MEMORYSTRUCTURES Algebra and Number Theory Algebraic structure Applied Mathematics Order (ring theory) Translation (geometry) 16G20 55N99 Theory of computation FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology Representation Theory (math.RT) Special case Representation (mathematics) Mathematics - Representation Theory Computer Science::Information Theory Mathematics |
| Zdroj: | Applicable Algebra in Engineering, Communication and Computing. |
| ISSN: | 1432-0622 0938-1279 |
| DOI: | 10.1007/s00200-021-00530-7 |
| Popis: | In order to better understand and to compare interleavings between persistence modules, we elaborate on the algebraic structure of interleavings in general settings. In particular, we provide a representation-theoretic framework for interleavings, showing that the category of interleavings under a fixed translation is isomorphic to the representation category of what we call a shoelace. Using our framework, we show that any two interleavings of the same pair of persistence modules are themselves interleaved. Furthermore, in the special case of persistence modules over $\mathbb{Z}$, we show that matchings between barcodes correspond to the interval-decomposable interleavings. Comment: 15 pages |
| Databáze: | OpenAIRE |
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