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research article
Combinatorial presentation of multidimensional persistent homology
Chacholski, W.
•
Scolamiero, M.
•
Vaccarino, F.
A multifiltration is a functor indexed by Nr that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the natural Nr-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 Nr-graded R[x(1),...,x(r)]-modules that can occur as R-spans of multifiltrations of sets are the direct sums of monomial ideals. (C) 2016 Elsevier B.V. All rights reserved.
Use this identifier to reference this record
Type
research article
Web of Science ID
WOS:000392783200002
Authors
Chacholski, W.
•
Scolamiero, M.
•
Vaccarino, F.
Publication date
2017
Publisher
Published in
Volume
221
Issue
5
Start page
1055
End page
1075
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
March 27, 2017