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URL: https://oeis.org/A056019

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A056019
Self-inverse 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
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.
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 + (((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 *)
CROSSREFS
Sequence in context: A368181 A375602 A275335 * A125963 A111269 A275657
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Jun 08 2000
STATUS
approved