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). [10.1016/j.jpaa.2016.09.001]

Combinatorial presentation of multidimensional persistent homology

SCOLAMIERO, MARTINA;VACCARINO, FRANCESCO
2017

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.
File in questo prodotto:
File Dimensione Formato  
Submission_8_2_2016.pdf

embargo fino al 30/09/2018

Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: Creative commons
Dimensione 493.16 kB
Formato Adobe PDF
493.16 kB Adobe PDF Visualizza/Apri
1409.7936v1.pdf

accesso aperto

Tipologia: 1. Preprint / submitted version [pre- review]
Licenza: PUBBLICO - Tutti i diritti riservati
Dimensione 554.23 kB
Formato Adobe PDF
554.23 kB Adobe PDF Visualizza/Apri
1-s2.0-S0022404916301475-main (1).pdf

non disponibili

Descrizione: Articolo principale
Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 541.25 kB
Formato Adobe PDF
541.25 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2651578
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo