  An infinite permutation is a linear ordering of the set of non-negative
integers. Generally, the properties of infinite permutations analogous to those
of infinite words show some resemblances and some differences between
permutations and words. In this paper, we define maximal pattern complexity for
infinite permutations and show that this complexity function is ultimately
constant if and only if the permutation is ultimately periodic. Then we
characterize the non-periodic permutations of minimal complexity (equal to n)
and find that they all are constructed with the use of Sturmian words.
