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%I #6 May 02 2017 22:17:15
%S 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,
%T 26,28,29,27,48,49,72,96,97,73,74,76,50,100,98,52,99,101,53,77,75,51,
%U 54,55,60,66,67,61,30,31,84,108,109,85,78,91,36,115,102,42,103,114,43
%N Permutation of nonnegative integers produced when the finite permutations listed by A055089 are subjected to Foata transform. Inverse of A065181.
%C 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.
%D 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.
%H Joe Buhler and R. L. Graham, <a href="http://www.cecm.sfu.ca/organics/papers/buhler/index.html">Juggling Drops and Descents</a>, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%p [seq(PermRevLexRank(Foata(PermRevLexUnrank(j))),j=0..119)];
%p 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;
%Y A065161-A065163 give cycle counts and max lengths. Cf. also A065183, A065184 and A055089 and A056019 for the requisite Maple procedures.
%K nonn
%O 0,3
%A _Antti Karttunen_, Oct 19 2001
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