# [seqfan] Re: Permutation inverse = inversion

Ron Hardin rhhardin at att.net
Mon Aug 30 12:32:29 CEST 2010

```Ignoring the bug off-the-array trailing 1, the inverse and inversion is
also the reverse, which may be the key.

rhhardin at mindspring.com
rhhardin at att.net (either)

----- Original Message ----
> From: Ron Hardin <rhhardin at att.net>
> To: seqfan at list.seqfan.eu
> Sent: Sun, August 29, 2010 10:35:50 PM
> Subject: [seqfan]  Permutation inverse = inversion
>
> A curiosity that just came  up
>
> 1,0,0,2,2,0,0,12,12,0,0,120,120,0,0,1680,1680,0,0,30240,30240
> Number  of permutations of 1..n p(i) with inverse permutation q(i) equal to the
>
> inversion: q(i)=n+1-p(i)
>
> eg. for n=8 the 12 permutations &  inverses
>
>  5 3 7 1 8 2 6 4 . 4 6 2 8 1 7 3 5 1
>  5 6 2 1 8 7 3 4 . 4 3 7  8 1 2 6 5 1
>  3 5 8 2 7 1 4 6 . 6 4 1 7 2 8 5 3 1
>  3 4 8 7 2 1 5 6 . 6 5 1  2 7 8 4 3 1
>  7 1 5 3 6 4 8 2 . 2 8 4 6 3 5 1 7 1
>  7 1 4 6 3 5 8 2 . 2 8 5  3 6 4 1 7 1
>  2 8 5 3 6 4 1 7 . 7 1 4 6 3 5 8 2 1
>  2 8 4 6 3 5 1 7 . 7 1 5  3 6 4 8 2 1
>  6 5 1 2 7 8 4 3 . 3 4 8 7 2 1 5 6 1
>  6 4 1 7 2 8 5 3 . 3 5 8  2 7 1 4 6 1
>  4 3 7 8 1 2 6 5 . 5 6 2 1 8 7 3 4 1
>  4 6 2 8 1 7 3 5 . 5 3 7  1 8 2 6 4 1
>
> the nonzero counts match
>
> http://www.research.att.com/~njas/sequences/A001813
>
>
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
>
>
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>

```