On the number of certain types of strongly restricted permutations

Abstract

Let p be a permutation of the set Nn={1, 2,...,n}. We introduce techniques for counting N(n; k, r, I), the number of Lehmer?s strongly restricted permutations of Nn satisfying the conditions ?k ? p(i)?i ? r (for arbitrary natural numbers k and r) and p(i) ? i I (for some set I). We show that N(n; 1, r, ?) is the Fibonacci (r + 1)-step number.