Combinatorial presentation of multidimensional persistent homology
نویسندگان
چکیده
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[x1, . . . , xr]-module structure on the homology of a multifiltration of simplicial complexes. To do that we study multifiltrations of sets and vector spaces. We prove in particular that the Nr-graded R[x1, . . . , xr]-modules that can occur as R-spans of multifiltrations of sets are the direct sums of monomial ideals.
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ورودعنوان ژورنال:
- CoRR
دوره abs/1409.7936 شماره
صفحات -
تاریخ انتشار 2014