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EnglishA multifiltration is a functor indexed by N^r that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the natural N^r-graded R[x_1,...,x_r]-module structure on the homology of a multifiltration of simplicial complexes. To do that we study multifiltrations of sets and R-modules. We prove in particular that the N^r-graded R[x_1,...,x_r]-modules that can occur as R-spans of multifiltrations of sets are the direct sums of monomial ideals.
http://hdl.handle.net/11583/2651578| Titolo: | Combinatorial presentation of multidimensional persistent homology |
| Autori: | |
| Data di pubblicazione: | 2017 |
| Rivista: | |
| Abstract: | A multifiltration is a functor indexed by N^r that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the natural N^r-graded R[x_1,...,x_r]-module structure on the homology of a multifiltration of simplicial complexes. To do that we study multifiltrations of sets and R-modules. We prove in particular that the N^r-graded R[x_1,...,x_r]-modules that can occur as R-spans of multifiltrations of sets are the direct sums of monomial ideals. |
| Digital Object Identifier (DOI): | 10.1016/j.jpaa.2016.09.001 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| Submission_8_2_2016.pdf | 2. Post-print | PUBBLICO - Licenza CC by-nc-nd | Embargo: 30/09/2018 Richiedi una copia | |
| 1409.7936v1.pdf | 1. Pre-print | PUBBLICO - Tutti i diritti riservati | Visibile a tuttiVisualizza/Apri |
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