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0
votes
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 \ …
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 …