[seqfan] Re: Q regarding comment in A000079 (Powers of 2)

Joerg Arndt arndt at jjj.de
Wed Jun 24 09:24:44 CEST 2009


* franktaw at netscape.net <franktaw at netscape.net> [Jun 24. 2009 17:09]:
> Well, of course, the original (with left) is also correct; just the 
> examples don't match it.
> 
> Franklin T. Adams-Watters
> 
> 

Jawohl!

...and the left<-->right swap goes with the inverse:

              ffact        perm            inv. perm       ffact(inv)
       1:    . 3 . .    [ 0 4 1 2 3 ]    [ 0 2 3 4 1 ]     . 1 1 1
       2:    . 2 . .    [ 0 3 1 2 4 ]    [ 0 2 3 1 4 ]     . 1 1 .
       3:    . 1 . .    [ 0 2 1 3 4 ]    [ 0 2 1 3 4 ]     . 1 . .
       4:    . 1 . 1    [ 0 2 1 4 3 ]    [ 0 2 1 4 3 ]     . 1 . 1
       5:    . . . 1    [ 0 1 2 4 3 ]    [ 0 1 2 4 3 ]     . . . 1
       6:    . . . .    [ 0 1 2 3 4 ]    [ 0 1 2 3 4 ]     . . . .
       7:    . . 1 .    [ 0 1 3 2 4 ]    [ 0 1 3 2 4 ]     . . 1 .
       8:    . . 2 .    [ 0 1 4 2 3 ]    [ 0 1 3 4 2 ]     . . 1 1
       9:    1 . 2 .    [ 1 0 4 2 3 ]    [ 1 0 3 4 2 ]     1 . 1 1
      10:    1 . 1 .    [ 1 0 3 2 4 ]    [ 1 0 3 2 4 ]     1 . 1 .
      11:    1 . . .    [ 1 0 2 3 4 ]    [ 1 0 2 3 4 ]     1 . . .
      12:    1 . . 1    [ 1 0 2 4 3 ]    [ 1 0 2 4 3 ]     1 . . 1
      13:    2 . . 1    [ 2 0 1 4 3 ]    [ 1 2 0 4 3 ]     1 1 . 1
      14:    2 . . .    [ 2 0 1 3 4 ]    [ 1 2 0 3 4 ]     1 1 . .
      15:    3 . . .    [ 3 0 1 2 4 ]    [ 1 2 3 0 4 ]     1 1 1 .
      16:    4 . . .    [ 4 0 1 2 3 ]    [ 1 2 3 4 0 ]     1 1 1 1

CAPTION:
Gray code for the permutations of 5 elements where no element lies more
than one place to the right of its position in the identical permutation.

(ffact := falling factorial (representation), i.e. inversion table).






More information about the SeqFan mailing list