Number of ways to partition a set with $n$ elements to $k$ subsets where at least one subset has $r$ elements
I'm familiar with Stirling numbers of the second kind to compute the number of ways to partition a set with $n$ elements into $k$ non-empty, disjoint subsets. However, there are combinations which I ...
I've done a couple of searches and haven't found a solution to this here, but if I've missed it please feel free to close the question! I was wondering how many different equivalence relations I ...
I came across some interesting propositions in some calculations I did and I was wondering if someone would be so kind as to provide some explanations of these phenomenon. We call an ordered ...
I'm reading Analytic Combinatorics [PDF] book by Flajolet and Sedgewick, and I can't figure out one of the steps in the derivation of the $P_n$ — number of partitions of size $n$ (or coefficients in ...