Practicalpart
New member
- Joined
- Aug 28, 2019
- Messages
- 5
(a) Find an exponential family F where the hands correspond to fixed-point-
free involutions. (That is, hands correspond to permutations that are both
involutions and also derangements.)
(b) Find the deck and hand enumerators for your exponential family F.
(c) Find the exponential generating function for the set of fixed-point-free invo-
lutions. (Your answer should be in closed form, with no infinite sums.)
So I came to conclusions that for the fixed point free involutions I can use the formula (2k-1)(2k-3)...1 where n=2k and this would equal to dn(number of elements in deck n)
Deck enumerator: D(x)= sum(dn * x^n /n!) Where n is even
Hand enumerator: H(x) = e^D(x)
My problem is I dont know if this is all correct and if it is how do i simplify D(x).
The class followed the book generatingfinctionology by wilf.
I am in the first year of university.
free involutions. (That is, hands correspond to permutations that are both
involutions and also derangements.)
(b) Find the deck and hand enumerators for your exponential family F.
(c) Find the exponential generating function for the set of fixed-point-free invo-
lutions. (Your answer should be in closed form, with no infinite sums.)
So I came to conclusions that for the fixed point free involutions I can use the formula (2k-1)(2k-3)...1 where n=2k and this would equal to dn(number of elements in deck n)
Deck enumerator: D(x)= sum(dn * x^n /n!) Where n is even
Hand enumerator: H(x) = e^D(x)
My problem is I dont know if this is all correct and if it is how do i simplify D(x).
The class followed the book generatingfinctionology by wilf.
I am in the first year of university.