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.
Combinatorial presentation of multidimensional persistent homology / Chacholski, W.; Scolamiero, Martina; Vaccarino, Francesco. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - STAMPA. - (2017).
Titolo: | Combinatorial presentation of multidimensional persistent homology |
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Data di pubblicazione: | 2017 |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jpaa.2016.09.001 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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Submission_8_2_2016.pdf | 2. Post-print / Author's Accepted Manuscript | ![]() | Visibile a tuttiVisualizza/Apri | |
1409.7936v1.pdf | 1. Preprint / Submitted Version | PUBBLICO - Tutti i diritti riservati | Visibile a tuttiVisualizza/Apri |
http://hdl.handle.net/11583/2651578