

A056019


Selfinverse infinite permutation which shows the position of each finite permutation's inverse permutation in A055089.


13



0, 1, 2, 4, 3, 5, 6, 7, 12, 18, 13, 19, 8, 10, 14, 20, 16, 22, 9, 11, 15, 21, 17, 23, 24, 25, 26, 28, 27, 29, 48, 49, 72, 96, 73, 97, 50, 52, 74, 98, 76, 100, 51, 53, 75, 99, 77, 101, 30, 31, 36, 42, 37, 43, 54, 55, 78, 102, 79, 103, 60, 66, 84, 108, 90, 114, 61, 67, 85
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OFFSET

0,3


COMMENTS

PermRevLexRank and PermRevLexUnrank have been modified from the algorithms PermLexRank and PermLexUnrank presented in the book "Combinatorial Algorithms, Generation, Enumeration and Search", by Donald L. Kreher and Douglas R. Stinson.


LINKS

Tilman Piesk, Table of n, a(n) for n = 0..5039
Index entries for sequences that are permutations of the natural numbers


FORMULA

[seq(PermRevLexRank(convert(invperm(convert(PermRevLexUnrank(j), 'disjcyc')), 'permlist', nops(PermRevLexUnrank(j)))), j=0..200)];


EXAMPLE

E.g. the permutation [2,3,1] is the 4th permutation (counting from 0th, the identity permutation) of A055089, its inverse permutation is [3,1,2] which is 3rd, thus a(4)=3 and a(3)=4.


MAPLE

PermRevLexRank := proc(pp) local p, n, i, j, r; p := pp; n := nops(p); r := 0; for j from n by 1 to 1 do r := r + (((jp[j])*((j1)!))); for i from 1 to (j1) do if(p[i] > p[j]) then p[i] := p[i]1; fi; od; od; RETURN(r); end;


MATHEMATICA

A056019 = Position[Ordering /@ #, #[[#2]]][[1, 1]]  1 &[Reverse@SortBy[Permutations@Range@Ceiling@InverseFunction[Factorial][# + 1], Reverse], # + 1] &; Array[A056019, 69, 0] (* JungHwan Min, Oct 10 2016 *)
A056019L = Ordering[Ordering /@ Permutations@Range@Ceiling@InverseFunction[Factorial][# + 1]]  1 &; A056019L[24] (* JungHwan Min, Oct 10 2016 *)


CROSSREFS

Sequence in context: A131042 A274631 A275335 * A125963 A111269 A275657
Adjacent sequences: A056016 A056017 A056018 * A056020 A056021 A056022


KEYWORD

nonn,changed


AUTHOR

Antti Karttunen, Jun 08 2000


STATUS

approved



