A065182 Permutation of nonnegative integers produced when the finite permutations listed by A055089 are subjected to Foata transform. Inverse of A065181.

0, 1, 2, 4, 5, 3, 6, 7, 12, 18, 19, 13, 14, 16, 8, 22, 20, 10, 21, 23, 11, 17, 15, 9, 24, 25, 26, 28, 29, 27, 48, 49, 72, 96, 97, 73, 74, 76, 50, 100, 98, 52, 99, 101, 53, 77, 75, 51, 54, 55, 60, 66, 67, 61, 30, 31, 84, 108, 109, 85, 78, 91, 36, 115, 102, 42, 103, 114, 43

Offset

0,3

Comments

Here we use a variant of Foata's transformation, which forms a new permutation by "inserting parentheses" at each left-right maxima, to delimit cycles.

References

I. M. Gessel and R. P. Stanley, Algebraic Enumeration, chapter 21 in Handbook of Combinatorics, Vol. 2, edited by R.L.Graham et al., The MIT Press, Mass, 1995, page 1045.

Links

Table of n, a(n) for n=0..68.

Joe Buhler and R. L. Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.

Index entries for sequences that are permutations of the natural numbers

Maple

[seq(PermRevLexRank(Foata(PermRevLexUnrank(j))), j=0..119)];
with(group); Foata := proc(p) local c, c1, i, m; c := []; c1 := []; m := 0; for i from 1 to nops(p) do if(p[i] > m) then if(nops(c1) > 1) then c := [op(c), c1]; fi; m := p[i]; c1 := []; fi; c1 := [op(c1), p[i]]; od; if(nops(c1) > 1) then c := [op(c), c1]; fi; RETURN(convert(c, 'permlist', nops(p))); end;

Crossrefs

A065161-A065163 give cycle counts and max lengths. Cf. also A065183, A065184 and A055089 and A056019 for the requisite Maple procedures.

Sequence in context: A276127 A182115 A362962 * A060120 A065183 A119791

Adjacent sequences: A065179 A065180 A065181 * A065183 A065184 A065185

Keyword

nonn

Author

Antti Karttunen, Oct 19 2001

Status

approved