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 A195931 The number of orbits in S_n by the action of Foata's bijection. 2
 1, 1, 2, 5, 16, 56, 236, 998, 4544, 20346 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. REFERENCES James Pfeiffer, personal communication. LINKS Dominique Foata and Marcel-Paul Schützenberger, Major Index and inversion number of permutations, Math. Nachr. 83 (1978), 143-159 EXAMPLE 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)] CROSSREFS Cf. A195931, A195924, A065161 Sequence in context: A147771 A052891 A052815 * A082789 A234278 A180678 Adjacent sequences:  A195928 A195929 A195930 * A195932 A195933 A195934 KEYWORD nonn,hard,more AUTHOR Austin Roberts, Oct 26 2011 STATUS approved

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Last modified February 19 13:03 EST 2020. Contains 332044 sequences. (Running on oeis4.)