0,3

Foata's bijection takes a permutation w with maj(w)=x to a permutation F(w) with inv(F(w))=x. Applying F repeatedly partitions the symmetric group into distinct orbits. F also preserves inverse descent sets.

James Pfeiffer, personal communication.

Table of n, a(n) for n=0..9.

Dominique Foata and Marcel-Paul Schützenberger, Major Index and inversion number of permutations, Math. Nachr. 83 (1978), 143-159

The orbits of S_4 are:

[(1, 2, 3, 4)]

[(2, 1, 3, 4)]

[(2, 3, 1, 4)]

[(2, 3, 4, 1)]

[(3, 2, 1, 4)]

[(3, 2, 4, 1)]

[(3, 4, 2, 1)]

[(4, 3, 2, 1)]

[(2, 1, 4, 3), (4, 2, 1, 3), (2, 4, 1, 3)]

[(2, 4, 3, 1), (4, 2, 3, 1)]

[(1, 3, 2, 4), (3, 1, 2, 4)]

[(1, 3, 4, 2), (3, 1, 4, 2), (3, 4, 1, 2)]

[(1, 4, 3, 2), (4, 3, 1, 2)]

[(4, 1, 3, 2)]

[(1, 2, 4, 3), (4, 1, 2, 3)]

[(1, 4, 2, 3)]

Cf. A195931, A195924, A065161

Sequence in context: A147771 A052891 A052815 * A082789 A234278 A180678

Adjacent sequences: A195928 A195929 A195930 * A195932 A195933 A195934

nonn,hard,more

Austin Roberts, Oct 26 2011

approved