This is the reverse-complement of pi.
In one-line notation, the reverse of a permutation is what you get by writing it backwards and the complement of a permutation is what you get when you replace each entry i by n−i+1. (In other words, one of these operations is multiplication by chi on the right, the other on the left.) The reverse-complement is what you get by doing both of these operations, or equivalently by giving the permutation matrix a half-turn. (Together with inversion, these operations generate the dihedral group acting on each permutation matrix.)
No comments:
Post a Comment