  We show that Han's bijection when restricted to permutations can be carried
out in terms of the cyclic major code and the cyclic inversion code. In other
words, it maps a permutation $\pi$ with a cyclic major code $(s_1, s_2, ...,
s_n)$ to a permutation $\sigma$ with a cyclic inversion code $(s_1,s_2, ...,
s_n)$. We also show that the fixed points of Han's map can be characterized by
the strong fixed points of Foata's second fundamental transformation. The
notion of strong fixed points is related to partial Foata maps introduced by
Bj\"orner and Wachs.

Combinatorics