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Answer by kimchi lover for Expected number of $1$s in a "similarity matrix"

You have to say more about the way points are assigned to clusters. Let $S_k$ be the size of the $k$-th cluster. Obviously $\sum S_k = M$, and you require $S_k\ge 1$. Your number of $1$s is $\sum_k...

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Expected number of $1$s in a "similarity matrix"

There are $p$ points given (the $n$th point is called $p_n$). These points are split into exactly $n$ clusters, where $1\le n\le p$. Of course there are many possibilities for the cluster sizes.Now...

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