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Number of permutations with a specified number of fixed points

see Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points
12 votes
5 answers
13k views

Number of permutations with a specified number of fixed points

Let $F(k,n)$ be the number of permutations of an n-element set that fix exactly $k$ elements. We know: $F(n,n) = 1$ $F(n-1,n) = 0$ $F(n-2,n) = \binom {n} {2}$ ... $F(0,n) = n! \cdot \sum_{k=0}^n \ …
Hans-Peter Stricker's user avatar
2 votes
0 answers
168 views

Enumeration and encoding of simplicial complexes

I'd like to know how to enumerate and encode all (abstract) simplicial complexes of a given kind. To start as simple as possible, consider the familiy $\mathcal{S}_n^{d}$ of simplicial complexes which …
Hans-Peter Stricker's user avatar