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A065182 Permutation of nonnegative integers produced when the finite permutations listed by A055089 are subjected to Foata transform. Inverse of A065181. 3
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 (list; graph; refs; listen; history; text; internal format)
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
Joe Buhler and R. L. Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 19 2001
STATUS
approved

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Last modified April 17 18:43 EDT 2024. Contains 371765 sequences. (Running on oeis4.)