Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A product of integer partitions   I present a bijection on integer partitions that leads to recursive
expressions, closed formulae and generating functions for the cardinality of
certain sets of partitions of a positive integer $n$. The bijection leads also
to a product on partitions that is associative with a natural grading thus
defining a free associative algebra on the set of integer partitions. As an
outcome of the computations, certain sets of integers appear that I call
difference sets and the product of the integers in a difference set is an
invariant for a family of sets of partitions. The main combinatorial objects
used in these constructions are the central hooks of the Ferrers diagrams of
partitions.

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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: physics