Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial presentation of multidimensional persistent homology   A multifiltration is a functor indexed by $\mathbb{N}^r$ that maps any
morphism to a monomorphism. The goal of this paper is to describe in an
explicit and combinatorial way the natural $\mathbb{N}^r$-graded $R[x_1,\ldots,
x_r]$-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 $\mathbb{N}^r$-graded $R[x_1,\ldots, x_r]$-modules
that can occur as $R$-spans of multifiltrations of sets are the direct sums of
monomial ideals.

36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org