Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partition number identities which are true for all set of parts   Let $B$ be an infinite subset of $\mathbf{N}$. When we consider partitions of
natural numbers into elements of $B$, a partition number without a restriction
of the number of equal parts can be expressed by partition numbers with a
restriction $\alpha$ of the number of equal parts. Although there are many way
of the expression, we prove that there exists a expression form such that this
expression form is true for all possible set $B$. This identities comes from
the partition numbers of natural numbers into
$\{1,\alpha,\alpha^2,\alpha^3,\cdots\}$. Furthermore, we prove that there exist
inverse forms of the expression forms. And we prove other similar identities.
The proofs in this paper are constructive.

33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph