Problem #12

A permutation f :{1,2,..., n} → {1,2,..., n} is said to be dispersive if {|f(1) − 1|, |f(2) − 2|,..., |f(n) − n|} = {0,1,..., n − 1}. For example, the permutation on the left is dispersive, while the one on the right is not. Let An denote the number of dispersive permutations on {0,1,..., n}. Can you find a formula for An ?

The solution will be posted shortly.

Back to the Archives

Back to the Math Department Homepage.