Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Investigation on Partitions with Equal Products   An ordered triple $(s,p,n)$ is called admissible if there exist two different
multisets $X=\{x_1,x_2,\dotsc,x_n\}$ and $Y=\{y_1,y_2,\dotsc,y_n\}$ such that
$X$ and $Y$ share the same sum $s$, the same product $p$, and the same size
$n$. We first count the number of $n$ such that $(s,p,n)$ are admissible for a
fixed $s$. We also fully characterize the values $p$ such that $(s,p,n)$ is
admissible. Finally, we consider the situation where $r$ different multisets
are needed, instead of just two. This project is also related to John Conway's
wizard puzzle from the 1960s.

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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga