ON THE NUMBER OF CERTAIN TYPES OF STRONGLY RESTRICTED PERMUTATIONS

Let p be a permutation of the set N-n = {1, 2,...,n}. We introduce techniques for counting N (n; k, r, I), the number of Lehmer's strongly restricted permutations of N n satisfying the conditions -k <= p (i) - i <= r (for arbitrary natural numbers k and r) and p (i) - i is not an element of I (for some set I). We show that N (n; 1; r;empty set) is the Fibonacci (r + 1)-step number.