A056019 Self-inverse infinite permutation which shows the position of each finite permutation's inverse permutation in A055089.

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

Offset: 0

Author

Antti Karttunen, Jun 08 2000

Keywords

• nonn
• look

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.

Examples

			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.
		

Links

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

Programs

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 + (((j-p[j])*((j-1)!))); for i from 1 to (j-1) do if(p[i] > p[j]) then p[i] := p[i]-1; fi; od; od; RETURN(r); end;
[seq(PermRevLexRank(convert(invperm(convert(PermRevLexUnrank(j), 'disjcyc')), 'permlist', nops(PermRevLexUnrank(j)))), j=0..200)];

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 *)