On generalized Fibonacci permutations
Alois Panholzer · Journal of Information and Optimization Sciences · 2003
We consider permutations σ, such that the property ∣(i)-i∣ ≤ N holds for all positions i (N ε N fixed). We show, that the number FN,n of permutations of length n which satisfy above restriction, is given as the solution of a linear recurrence with constant coefficients of order (2NN ) for n. We describe this recurrence and show further the asymptotic expansion FN,n ˜ c N ρn Nwith the bounds 1/2 ≤ ρN/N +1 ≤ 1.