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## Saturday, April 24, 2010

### Stirling numbers of the first kind

$\begin{array}{lllll} 1 &&&&\\ 0 & 1 &&&\\ 0 & 1 & 1 &&\\ 0 & 2 & 3 & 1 &\\ 0 & 6 & 11 & 6 & 1 \end{array}$
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.

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Mathematics: is it the fabric of MEST?
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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)