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Proposition: Factorials and Stirling Numbers of the First Kind
The number of permutations of $n\ge 0$ objects corresponds to the number of ways to arrange $n$ objects into $r$ cycles, summed up over $r,$ more formally
\[n!=\sum_{r=0}^n \left[\begin{array}{c}n\\r\end{array}\right],\quad\quad(n\ge 0).\]
Table of Contents
Proofs: 1
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References
Bibliography
 Aigner, Martin: "Diskrete Mathematik", vieweg studium, 1993