$

\begin{array}{lllll}

1 &&&&\\

0 & 1 &&&\\

0 & 1 & 1 &&\\

0 & 2 & 3 & 1 &\\

0 & 6 & 11 & 6 & 1

\end{array}

$

A stirling number of the first kind is the number of permutations of {1, 2, ..., n } with k permutation cycles. Take for example the permutations of {1,2,3 }:

123 - (1)(2)(3)

132 - (1)(23)

213 - (12)(3)

231 - (132)

312 - (132)

321 - (13)(2)

each line consists of the same permutation but in different notation. After the - I noted the permutation in cycle notation. So there are 2 3-permutations of 1 cycle, 3 of 2 cycles and 1 of 3 cycles.

2-2018 Teaching by misleading

3 weeks ago

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