Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of direct-sum decompositions of a finite vector space   The theory of q-analogs develops many combinatorial formulas for finite
vector spaces over a finite field with q elements--all in analogy with formulas
for finite sets (which are the special case of q=1). A direct-sum decomposition
of a finite vector space is the vector space analogue of a set partition. This
paper develops the formulas for the number of direct-sum decompositions that
are the q-analogs of the formulas for: (1) the number of set partitions with a
given number partition signature; (2) the number of set partitions of an
n-element set with m blocks (the Stirling numbers of the second kind); and (3)
for the total number of set partitions of an n-element set (the Bell numbers).

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The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th