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authorPaul Jungeblut <paul.jungeblut@gmail.com>2017-10-31 22:17:14 +0100
committerPaul Jungeblut <paul.jungeblut@gmail.com>2017-10-31 22:17:14 +0100
commit899ad545406e3e4aa7a18089383a2113f2260f08 (patch)
tree7b4dd6165a2a046ed48f3fd8905f3298e5558f8b /math
parentca782cdf2cfe011a7fb73b8b8299cc614c8af251 (diff)
Adding another formular to count the number of derangements.
Diffstat (limited to 'math')
-rw-r--r--math/math.tex4
1 files changed, 3 insertions, 1 deletions
diff --git a/math/math.tex b/math/math.tex
index 54f2a38..8fc408c 100644
--- a/math/math.tex
+++ b/math/math.tex
@@ -559,9 +559,11 @@ Anzahl der Teilmengen von $\mathbb{N}$, die sich zu $n$ aufaddieren mit maximale
\#Wälder mit $k$ gewurzelten Bäumen &
$\frac{k}{n}\binom{n}{k}n^{n-k}$ \\
- Dearangements &
+ Derangements &
$!n = (n - 1)(!(n - 1) + !(n - 2))$ \\
&
+ $!n = \left\lfloor\frac{n!}{e} + \frac{1}{2}\right\rfloor$ \\
+ &
$\lim\limits_{n \to \infty} \frac{!n}{n!} = \frac{1}{e}$ \\
\bottomrule
\end{tabular}