A065181 Permutation of nonnegative integers produced when the finite permutations listed by A055089 are subjected to inverse of Foata's transformation. Inverse of A065182.
0, 1, 2, 5, 3, 4, 6, 7, 14, 23, 17, 20, 8, 11, 12, 22, 13, 21, 9, 10, 16, 18, 15, 19, 24, 25, 26, 29, 27, 28, 54, 55, 86, 119, 95, 110, 62, 71, 78, 116, 79, 113, 65, 68, 92, 102, 89, 103, 30, 31, 38, 47, 41, 44, 48, 49, 84, 118, 94, 108, 50, 53, 80, 117, 83, 109, 51, 52
Offset: 0
Keywords
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.
- Index entries for sequences that are permutations of the natural numbers
Crossrefs
Programs
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Maple
[seq(PermRevLexRank(FoataInv(PermRevLexUnrank(j))),j=0..119)]; with(group); FoataInv := p -> map(op, sort([op(map(RotCycleLargestFirst,convert(p,`disjcyc`))),op(FixedCycles(p))], sortbyfirst)); sortbyfirst := (a,b) -> `if`((a[1] < b[1]),true,false); FindLargest := proc(a) local i,m; m := 0; for i from 1 to nops(a) do if(0 = m) then m := i; else if(a[i] > a[m]) then m := i; fi; fi; od; RETURN(m); end; RotCycleLargestFirst := proc(c) local x; x := FindLargest(c); if(x <= 1) then RETURN(c); else RETURN([op(c[x..nops(c)]),op(c[1..(x-1)])]); fi; end; FixedCycles := proc(p) local a,i; a := []; for i from 1 to nops(p) do if(p[i] = i) then a := [op(a),[i]]; fi; od; RETURN(a); end;
Comments