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$\pi\in S_n$, $\mathrm{desc}(\pi):=\{i\in[n-1]: \pi_{i+1}<\pi_i\}$. $S\subset[n-1]$ and $S$ of size $k$. Could you help me to calculate the following numbers, please?

1) The number of permutations $\pi\in S_n$ with $\mathrm{desc}(\pi)\supseteq S$.

2) The number of permutations $\pi\in S_n$ with $\mathrm{desc}(\pi)=S$.

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    By "understand the following numbers", do you mean understand their definitions, or understand how to calculate them?2011-11-11
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    calculate, I edited the question2011-11-11
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    This is relevant and answers part 2: http://math.stackexchange.com/questions/77391/the-number-of-permutations-with-descents-at-specified-positions-1-leq-a-1-a/77445#774452011-11-11
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    A minor note: A more widespread notation is $\mathrm{Des}(\pi)$ for the descent set of $\pi$ and $\mathrm{des}(\pi)=|\mathrm{Des}(\pi)|$ for the number of descents of $\pi$.2017-11-14

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