Chacholski, W.
Scolamiero, M.
Vaccarino, F.
Combinatorial presentation of multidimensional persistent homology
Journal Of Pure And Applied Algebra
Journal Of Pure And Applied Algebra
Journal Of Pure And Applied Algebra
Journal Of Pure And Applied Algebra
21
221
5
2017
2017
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.
Elsevier
0022-4049
Journal Of Pure And Applied Algebra
Journal Articles
10.1016/j.jpaa.2016.09.001