A permutation π = (π 1π 2…π n) of {1, 2,…, n} is called k-sorted if and only if i −π i ≤ k, for all 1 ≤ i ≤ n.We propose an algorithm for generating the set of all k-sorted permutations of {1, 2,…, n} in lexicographic order. An inversion occurs between a pair of ( i π , j π ) if i < j but i π > π j . Let I(n, k) denote the maximum number of inversions in k-sorted permutations. For k-sorted permutations with weakly restricted displacements, i.e., |n / 2| ≤ k ≤ n −1, we propose a concise formula of I(n, k) by using the generating functions approach.