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\title{Cardinality of Number Partitions}
\author{Lukas Bulwahn}
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\begin{abstract}
This entry provides a basic library for number partitions, defines the
two-argument partition function through its recurrence relation and relates
this partition function to the cardinality of number partitions. The main
proof shows that the recursively-defined partition function with arguments
$n$ and $k$ equals the cardinality of number partitions of $n$ with exactly
$k$ parts. The combinatorial proof follows the proof sketch of Theorem~2.4.1
in Mazur's textbook ``Combinatorics: A Guided Tour''~\cite{mazur-2010}. This
entry can serve as starting point for various more intrinsic properties about
number partitions, the partition function and related recurrence relations.

\end{abstract}

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